{"id":1855,"date":"2026-05-21T09:28:00","date_gmt":"2026-05-21T09:28:00","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1855"},"modified":"2026-08-26T12:00:31","modified_gmt":"2026-08-26T06:30:31","slug":"inverse-trigonometric-functions-exercise-2-2-solutions","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/inverse-trigonometric-functions-exercise-2-2-solutions\/","title":{"rendered":"Inverse Trigonometric Functions Exercise 2.2 Solutions"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-3482327769\"><div id=\"mymoc-3871006056\"><a href=\"https:\/\/amzn.to\/4v5gV6P\" aria-label=\"calculators\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators.png 1302w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-300x99.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-1024x338.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-768x254.png 768w\" sizes=\"(max-width: 1302px) 100vw, 1302px\" width=\"1302\" height=\"430\"><\/a><\/div><\/div>\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">In this post, students can find complete step-by-step solutions for Class 12 Maths Chapter 2 Exercise 2.2 &ndash; Inverse Trigonometric Functions based on the latest NCERT syllabus. This exercise includes inverse trigonometric identities, simplification of expressions, proving formulas, and solving equations in an easy and exam-oriented format.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Item<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Board<\/td><td>NCERT \/ CBSE<\/td><\/tr><tr><td>Class<\/td><td>12<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Chapter<\/td><td>Inverse Trigonometric Functions<\/td><\/tr><tr><td>Exercise<\/td><td>2.2<\/td><\/tr><tr><td>Main Topics<\/td><td>Identities &amp; Simplifications<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Inverse Trigonometric Identities<\/li>\n\n\n\n<li>Triple Angle Formula<\/li>\n\n\n\n<li>Simplification of Expressions<\/li>\n\n\n\n<li>Principal Value Branch<\/li>\n\n\n\n<li>tan&#8315;&sup1; Identities<\/li>\n\n\n\n<li>sin&#8315;&sup1; and cos&#8315;&sup1; Relations<\/li>\n\n\n\n<li>Solving Trigonometric Equations<\/li>\n\n\n\n<li>Principal Values<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The exercise focuses on proving identities and simplifying inverse trigonometric expressions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Triple Angle Identity<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><mn>3<\/mn><mi>&theta;<\/mi><mo>=<\/mo><mn>3<\/mn><mi>sin<\/mi><mo>&#8289;<\/mo><mi>&theta;<\/mi><mo>&minus;<\/mo><mn>4<\/mn><msup><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>&theta;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sin3\\theta=3\\sin\\theta-4\\sin^3\\theta<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Triple Angle Cosine Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><mn>3<\/mn><mi>&theta;<\/mi><mo>=<\/mo><mn>4<\/mn><msup><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>&theta;<\/mi><mo>&minus;<\/mo><mn>3<\/mn><mi>cos<\/mi><mo>&#8289;<\/mo><mi>&theta;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\cos3\\theta=4\\cos^3\\theta-3\\cos\\theta<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Tangent Addition Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>+<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><mi>A<\/mi><mo>+<\/mo><mi>tan<\/mi><mo>&#8289;<\/mo><mi>B<\/mi><\/mrow><mrow><mn>1<\/mn><mo>&minus;<\/mo><mi>tan<\/mi><mo>&#8289;<\/mo><mi>A<\/mi><mi>tan<\/mi><mo>&#8289;<\/mo><mi>B<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\tan(A+B)=\\frac{\\tan A+\\tan B}{1-\\tan A\\tan B}<\/annotation><\/semantics><\/math>&#8203;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Principal Value Range of tan&#8315;&sup1;x<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>x<\/mi><mo>&isin;<\/mo><mrow><mo fence=\"true\">(<\/mo><mo>&minus;<\/mo><mfrac><mi>&pi;<\/mi><mn>2<\/mn><\/mfrac><mo separator=\"true\">,<\/mo><mfrac><mi>&pi;<\/mi><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}x\\in\\left(-\\frac{\\pi}{2},\\frac{\\pi}{2}\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-step Solutions<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/relations-and-functions-exercise-1-1-solutions-class-12\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Relations and Functions Exercise 1.1 Solutions Class 12<\/span><\/a><\/div><p class=\"wp-block-paragraph\">Prove that:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><msup><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>x<\/mi><mo>=<\/mo><msup><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>x<\/mi><mo>&minus;<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">3\\sin^{-1}x=\\sin^{-1}(3x-4x^3)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x = sin&theta;<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&theta; = sin&#8315;&sup1;x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Using triple angle identity:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><mn>3<\/mn><mi>&theta;<\/mi><mo>=<\/mo><mn>3<\/mn><mi>sin<\/mi><mo>&#8289;<\/mo><mi>&theta;<\/mi><mo>&minus;<\/mo><mn>4<\/mn><msup><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>&theta;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sin3\\theta=3\\sin\\theta-4\\sin^3\\theta<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/relations-and-functions-exercise-1-2-solutions-class-12\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Relations and Functions Exercise 1.2 Solutions Class 12<\/span><\/a><\/div><p class=\"wp-block-paragraph\">Substituting:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sin3&theta; = 3x &minus; 4x&sup3;<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Taking inverse sine:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>3&theta; = sin&#8315;&sup1;(3x&minus;4x&sup3;)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-3925593612\"><div id=\"mymoc-2720792784\"><a href=\"https:\/\/amzn.to\/4upqwUD\" aria-label=\"laptop-1\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1-300x91.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1-1024x310.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1-768x233.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"395\"><\/a><\/div><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code>3sin&#8315;&sup1;x = sin&#8315;&sup1;(3x&minus;4x&sup3;)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Prove that:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><msup><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>x<\/mi><mo>=<\/mo><msup><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>&minus;<\/mo><mn>3<\/mn><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">3\\cos^{-1}x=\\cos^{-1}(4x^3-3x)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x = cos&theta;<\/code><\/pre>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/miscellaneous-exercise-solutions-class-12-relations-functions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Miscellaneous Exercise Solutions Class 12 Relations Functions<\/span><\/a><\/div><p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&theta; = cos&#8315;&sup1;x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Using triple angle identity:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><mn>3<\/mn><mi>&theta;<\/mi><mo>=<\/mo><mn>4<\/mn><msup><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>&theta;<\/mi><mo>&minus;<\/mo><mn>3<\/mn><mi>cos<\/mi><mo>&#8289;<\/mo><mi>&theta;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\cos3\\theta=4\\cos^3\\theta-3\\cos\\theta<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>cos3&theta; = 4x&sup3;&minus;3x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Taking inverse cosine:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>3&theta; = cos&#8315;&sup1;(4x&sup3;&minus;3x)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence proved.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msqrt><mrow><mn>1<\/mn><mo>+<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><mi>x<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}\\left(\\frac{\\sqrt{1+x^2}-1}{x}\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Multiply numerator and denominator appropriately.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After simplification:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>= tan&#8315;&sup1;[x\/(&radic;(1+x&sup2;)+1)]<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Using tangent half-angle identity:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = &frac12; tan&#8315;&sup1;x<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-922-1024x819.png\" alt=\"\" class=\"wp-image-6838\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-922-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-922-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-922-767x614.png 767w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-922-250x200.png 250w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-922.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><msqrt><mfrac><mrow><mn>1<\/mn><mo>&minus;<\/mo><mi>cos<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mi>cos<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><\/mrow><\/mfrac><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}\\sqrt{\\frac{1-\\cos x}{1+\\cos x}}<\/annotation><\/semantics><\/math>&#8203;&#8203;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using identity:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mrow><mn>1<\/mn><mo>&minus;<\/mo><mi>cos<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mi>cos<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><\/mrow><\/mfrac><mo>=<\/mo><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mn>2<\/mn><\/msup><mfrac><mi>x<\/mi><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1-\\cos x}{1+\\cos x}=\\tan^2\\frac{x}{2}<\/annotation><\/semantics><\/math>&#8203;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&radic;[(1&minus;cosx)\/(1+cosx)] = tan(x\/2)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = x\/2<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mi>sin<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><\/mrow><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><mo>+<\/mo><mi>sin<\/mi><mo>&#8289;<\/mo><mi>x<\/mi><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}\\left(\\frac{\\cos x-\\sin x}{\\cos x+\\sin x}\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Divide numerator and denominator by:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>cosx<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>= tan&#8315;&sup1;[(1&minus;tanx)\/(1+tanx)]<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Using formula:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan(A&minus;B)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = &pi;\/4 &minus; x<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mi>x<\/mi><msqrt><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}\\left(\\frac{x}{\\sqrt{a^2-x^2}}\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Put:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x = a sin&theta;<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&radic;(a&sup2;&minus;x&sup2;)=a cos&theta;<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan&#8315;&sup1;[tan&theta;]=&theta;<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = sin&#8315;&sup1;(x\/a)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 7<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><mn>3<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mi>x<\/mi><mo>&minus;<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><\/mrow><mrow><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>&minus;<\/mo><mn>3<\/mn><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}\\left(\\frac{3a^2x-x^3}{a^3-3ax^2}\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Put:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x = a tan&theta;<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Using triple angle formula:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan3&theta; = (3tan&theta;&minus;tan&sup3;&theta;)\/(1&minus;3tan&sup2;&theta;)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = 3tan&#8315;&sup1;(x\/a)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 8<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find the value of:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\">[<\/mo><mn>2<\/mn><mi>cos<\/mi><mo>&#8289;<\/mo><mrow><mo fence=\"true\">(<\/mo><mn>2<\/mn><msup><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo fence=\"true\">]<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}\\left[2\\cos\\left(2\\sin^{-1}\\frac12\\right)\\right]<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We know:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sin&#8315;&sup1;(1\/2)=&pi;\/6<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>2(&pi;\/6)=&pi;\/3<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Now:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>cos(&pi;\/3)=1\/2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>2 &times; 1\/2 = 1<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = tan&#8315;&sup1;(1)=&pi;\/4<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 9<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find the value of the expression.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"777\" height=\"125\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-24.png\" alt=\"image\" class=\"wp-image-1856\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-24.png 777w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-24-300x48.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-24-768x124.png 768w\" sizes=\"(max-width: 777px) 100vw, 777px\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using standard inverse trigonometric identities and simplification:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = &frac12; tan&#8315;&sup1;(x+y)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 10<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi>sin<\/mi><mo>&#8289;<\/mo><mfrac><mrow><mn>2<\/mn><mi>&pi;<\/mi><\/mrow><mn>3<\/mn><\/mfrac><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\sin^{-1}(\\sin\\frac{2\\pi}{3})<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We know:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sin(2&pi;\/3)=&radic;3\/2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Principal value branch of:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sin&#8315;&sup1;x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>[&minus;&pi;\/2, &pi;\/2]<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = &pi;\/3<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 11<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi>tan<\/mi><mo>&#8289;<\/mo><mfrac><mrow><mn>3<\/mn><mi>&pi;<\/mi><\/mrow><mn>4<\/mn><\/mfrac><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}(\\tan\\frac{3\\pi}{4})<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We know:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan(3&pi;\/4)=&minus;1<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan&#8315;&sup1;(&minus;1)=&minus;&pi;\/4<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 12<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"296\" height=\"99\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-25.png\" alt=\"image\" class=\"wp-image-1857\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-923-1024x819.png\" alt=\"\" class=\"wp-image-6850\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-923-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-923-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-923-767x614.png 767w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-923-250x200.png 250w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-923.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 13<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Evaluate:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>cos<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi>cos<\/mi><mo>&#8289;<\/mo><mfrac><mrow><mn>7<\/mn><mi>&pi;<\/mi><\/mrow><mn>6<\/mn><\/mfrac><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\cos^{-1}(\\cos\\frac{7\\pi}{6})<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Since:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>cos(7&pi;\/6)=&minus;&radic;3\/2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Principal value of cosine inverse lies in:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>[0, &pi;]<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = 5&pi;\/6<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Correct option:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(B)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 14<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Evaluate:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"432\" height=\"91\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-26.png\" alt=\"image\" class=\"wp-image-1858\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-26.png 432w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-26-300x63.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925-1024x683.png\" alt=\"\" class=\"wp-image-6855\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925-250x167.png 250w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925-450x300.png 450w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-925.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 15<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Evaluate:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><msqrt><mn>3<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo>&minus;<\/mo><msup><mrow><mi>cot<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mo>&minus;<\/mo><msqrt><mn>3<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}(\\sqrt3)-\\cot^{-1}(-\\sqrt3)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We know:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan&#8315;&sup1;(&radic;3)=&pi;\/3<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">and:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>cot&#8315;&sup1;(&minus;&radic;3)=5&pi;\/6<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&pi;\/3&minus;5&pi;\/6<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = &minus;&pi;\/2<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924-1024x683.png\" alt=\"\" class=\"wp-image-6853\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924-250x167.png 250w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924-450x300.png 450w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-924.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ignoring principal value ranges<\/li>\n\n\n\n<li>Confusing inverse with reciprocal<\/li>\n\n\n\n<li>Wrong use of triple angle formulas<\/li>\n\n\n\n<li>Errors in simplification<\/li>\n\n\n\n<li>Forgetting domain conditions<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Memorize standard inverse trigonometric values.<\/li>\n\n\n\n<li>Practice tangent addition identities.<\/li>\n\n\n\n<li>Always check principal branch.<\/li>\n\n\n\n<li>Use substitutions carefully.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Range of:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. [0,&pi;]<br>B. (&minus;&pi;\/2, &pi;\/2)<br>C. R<br>D. (0,2&pi;)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B. (&minus;&pi;\/2, &pi;\/2)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Value of:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>sin<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\sin^{-1}\\frac12<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. &pi;\/6<br>B. &pi;\/4<br>C. &pi;\/3<br>D. &pi;\/2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A. &pi;\/6<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Value of:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mi>tan<\/mi><mo>&#8289;<\/mo><\/mrow><mrow><mo>&minus;<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\tan^{-1}(1)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. &pi;<br>B. &pi;\/2<br>C. &pi;\/4<br>D. 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. &pi;\/4<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">What is principal value branch?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The restricted range chosen for inverse trigonometric functions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">What is the range of tan&#8315;&sup1;x?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">(<\/mo><mo>&minus;<\/mo><mfrac><mi>&pi;<\/mi><mn>2<\/mn><\/mfrac><mo separator=\"true\">,<\/mo><mfrac><mi>&pi;<\/mi><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(-\\frac{\\pi}{2},\\frac{\\pi}{2}\\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Is sin&#8315;&sup1;x equal to 1\/sinx?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">No.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sin&#8315;&sup1;x means inverse sine function.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Why are domains restricted?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">To make trigonometric functions one-one and invertible.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">CTA (Call To Action)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#128216; Prepare Smarter with MyMockMate!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Chapter-wise NCERT Solutions<br>&#9989; Important Notes &amp; MCQs<br>&#9989; Online Mock Tests<br>&#9989; Instant Result &amp; Analysis<br>&#9989; CBSE Board Preparation<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start learning now on <a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.mymockmate.com?utm_source=chatgpt.com\">MyMockMate<\/a><\/p>\n<div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-477633914\"><div id=\"mymoc-362983266\"><a href=\"https:\/\/amzn.to\/43YYZi3\" aria-label=\"smart-phones\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-300x76.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-1024x259.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-768x194.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"329\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Short Intro In this post, students can find complete step-by-step solutions for Class 12 Maths Chapter 2 Exercise 2.2 &ndash; Inverse Trigonometric Functions based on&#8230;<\/p>\n","protected":false},"author":1,"featured_media":1859,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":""},"categories":[7,8],"tags":[],"class_list":["post-1855","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-12","category-maths"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/Inverse-Trigonometric-Functions-Exercise-2.2-Solutions.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1855","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=1855"}],"version-history":[{"count":5,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1855\/revisions"}],"predecessor-version":[{"id":6856,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1855\/revisions\/6856"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1859"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}