{"id":1855,"date":"2026-05-21T09:28:00","date_gmt":"2026-05-21T09:28:00","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1855"},"modified":"2026-05-21T09:28:04","modified_gmt":"2026-05-21T09:28:04","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":"\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 \u2013 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\u207b\u00b9 Identities<\/li>\n\n\n\n<li>sin\u207b\u00b9 and cos\u207b\u00b9 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>\u2061<\/mo><mn>3<\/mn><mi>\u03b8<\/mi><mo>=<\/mo><mn>3<\/mn><mi>sin<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/mi><mo>\u2212<\/mo><mn>4<\/mn><msup><mrow><mi>sin<\/mi><mo>\u2061<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>\u03b8<\/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>\u2061<\/mo><mn>3<\/mn><mi>\u03b8<\/mi><mo>=<\/mo><mn>4<\/mn><msup><mrow><mi>cos<\/mi><mo>\u2061<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>\u03b8<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mi>cos<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/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>\u2061<\/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>\u2061<\/mo><mi>A<\/mi><mo>+<\/mo><mi>tan<\/mi><mo>\u2061<\/mo><mi>B<\/mi><\/mrow><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>tan<\/mi><mo>\u2061<\/mo><mi>A<\/mi><mi>tan<\/mi><mo>\u2061<\/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>\u200b<\/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\u207b\u00b9x<\/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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>x<\/mi><mo>\u2208<\/mo><mrow><mo fence=\"true\">(<\/mo><mo>\u2212<\/mo><mfrac><mi>\u03c0<\/mi><mn>2<\/mn><\/mfrac><mo separator=\"true\">,<\/mo><mfrac><mi>\u03c0<\/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<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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>x<\/mi><mo>=<\/mo><msup><mrow><mi>sin<\/mi><mo>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>x<\/mi><mo>\u2212<\/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\u03b8<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03b8 = sin\u207b\u00b9x<\/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>\u2061<\/mo><mn>3<\/mn><mi>\u03b8<\/mi><mo>=<\/mo><mn>3<\/mn><mi>sin<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/mi><mo>\u2212<\/mo><mn>4<\/mn><msup><mrow><mi>sin<\/mi><mo>\u2061<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>\u03b8<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sin3\\theta=3\\sin\\theta-4\\sin^3\\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>sin3\u03b8 = 3x \u2212 4x\u00b3<\/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\u03b8 = sin\u207b\u00b9(3x\u22124x\u00b3)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>3sin\u207b\u00b9x = sin\u207b\u00b9(3x\u22124x\u00b3)<\/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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>x<\/mi><mo>=<\/mo><msup><mrow><mi>cos<\/mi><mo>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/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\u03b8<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03b8 = cos\u207b\u00b9x<\/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>\u2061<\/mo><mn>3<\/mn><mi>\u03b8<\/mi><mo>=<\/mo><mn>4<\/mn><msup><mrow><mi>cos<\/mi><mo>\u2061<\/mo><\/mrow><mn>3<\/mn><\/msup><mi>\u03b8<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mi>cos<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/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\u03b8 = 4x\u00b3\u22123x<\/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\u03b8 = cos\u207b\u00b9(4x\u00b3\u22123x)<\/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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/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>\u2212<\/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\u207b\u00b9&#91;x\/(\u221a(1+x\u00b2)+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 = \u00bd tan\u207b\u00b9x<\/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 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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><msqrt><mfrac><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>cos<\/mi><mo>\u2061<\/mo><mi>x<\/mi><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mi>cos<\/mi><mo>\u2061<\/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>\u200b\u200b<\/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>\u2212<\/mo><mi>cos<\/mi><mo>\u2061<\/mo><mi>x<\/mi><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><mi>cos<\/mi><mo>\u2061<\/mo><mi>x<\/mi><\/mrow><\/mfrac><mo>=<\/mo><msup><mrow><mi>tan<\/mi><mo>\u2061<\/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>\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u221a&#91;(1\u2212cosx)\/(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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><mi>cos<\/mi><mo>\u2061<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mi>sin<\/mi><mo>\u2061<\/mo><mi>x<\/mi><\/mrow><mrow><mi>cos<\/mi><mo>\u2061<\/mo><mi>x<\/mi><mo>+<\/mo><mi>sin<\/mi><mo>\u2061<\/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\u207b\u00b9&#91;(1\u2212tanx)\/(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\u2212B)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = \u03c0\/4 \u2212 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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/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>\u2212<\/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\u03b8<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u221a(a\u00b2\u2212x\u00b2)=a cos\u03b8<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan\u207b\u00b9&#91;tan\u03b8]=\u03b8<\/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\u207b\u00b9(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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/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>\u2212<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><\/mrow><mrow><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/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\u03b8<\/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\u03b8 = (3tan\u03b8\u2212tan\u00b3\u03b8)\/(1\u22123tan\u00b2\u03b8)<\/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\u207b\u00b9(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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mrow><mo fence=\"true\">[<\/mo><mn>2<\/mn><mi>cos<\/mi><mo>\u2061<\/mo><mrow><mo fence=\"true\">(<\/mo><mn>2<\/mn><msup><mrow><mi>sin<\/mi><mo>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/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\u207b\u00b9(1\/2)=\u03c0\/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(\u03c0\/6)=\u03c0\/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(\u03c0\/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 \u00d7 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\u207b\u00b9(1)=\u03c0\/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 fetchpriority=\"high\" 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\" title=\"Inverse Trigonometric Functions Exercise 2.2 Solutions\" 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 = \u00bd tan\u207b\u00b9(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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi>sin<\/mi><mo>\u2061<\/mo><mfrac><mrow><mn>2<\/mn><mi>\u03c0<\/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\u03c0\/3)=\u221a3\/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\u207b\u00b9x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;\u2212\u03c0\/2, \u03c0\/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 = \u03c0\/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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi>tan<\/mi><mo>\u2061<\/mo><mfrac><mrow><mn>3<\/mn><mi>\u03c0<\/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\u03c0\/4)=\u22121<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tan\u207b\u00b9(\u22121)=\u2212\u03c0\/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\" title=\"Inverse Trigonometric Functions Exercise 2.2 Solutions\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using standard values:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Answer = \u03c0\/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 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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mi>cos<\/mi><mo>\u2061<\/mo><mfrac><mrow><mn>7<\/mn><mi>\u03c0<\/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\u03c0\/6)=\u2212\u221a3\/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>&#91;0, \u03c0]<\/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\u03c0\/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 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\" title=\"Inverse Trigonometric Functions Exercise 2.2 Solutions\" 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<p class=\"wp-block-paragraph\">Since:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sin\u207b\u00b9(1\/2)=\u03c0\/6<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>sin(\u03c0\/3\u2212\u03c0\/6)=sin(\u03c0\/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 = 1\/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 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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><msqrt><mn>3<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><msup><mrow><mi>cot<\/mi><mo>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/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\u207b\u00b9(\u221a3)=\u03c0\/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\u207b\u00b9(\u2212\u221a3)=5\u03c0\/6<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c0\/3\u22125\u03c0\/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 = \u2212\u03c0\/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\">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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/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,\u03c0]<br>B. (\u2212\u03c0\/2, \u03c0\/2)<br>C. R<br>D. (0,2\u03c0)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B. (\u2212\u03c0\/2, \u03c0\/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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/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. \u03c0\/6<br>B. \u03c0\/4<br>C. \u03c0\/3<br>D. \u03c0\/2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A. \u03c0\/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>\u2061<\/mo><\/mrow><mrow><mo>\u2212<\/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. \u03c0<br>B. \u03c0\/2<br>C. \u03c0\/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. \u03c0\/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\u207b\u00b9x?<\/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>\u2212<\/mo><mfrac><mi>\u03c0<\/mi><mn>2<\/mn><\/mfrac><mo separator=\"true\">,<\/mo><mfrac><mi>\u03c0<\/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\u207b\u00b9x 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\u207b\u00b9x 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\">\ud83d\udcd8 Prepare Smarter with MyMockMate!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Chapter-wise NCERT Solutions<br>\u2705 Important Notes &amp; MCQs<br>\u2705 Online Mock Tests<br>\u2705 Instant Result &amp; Analysis<br>\u2705 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\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","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<\/p>\n","protected":false},"author":1,"featured_media":1859,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_angie_page":false,"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"page_builder":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[7,100,8],"tags":[],"class_list":["post-1855","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-12","category-inverse-trigonometric-functions","category-maths"],"jetpack_publicize_connections":[],"_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":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1855\/revisions"}],"predecessor-version":[{"id":1860,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1855\/revisions\/1860"}],"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}]}}