Mathematics · Textbook solutions

Inverse Trigonometric Functions

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 49 questions

2.2 Basic Concepts

16 q

Solved Examples

Worked · 2

2.1 Eg.1 $\sin^{-1}\left(\frac{1}{\sqrt{2}}\right)$
2.1 Eg.2 $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$

Exercise 2.1

Practice · 14

Ex 2.1 Q1 $\sin^{-1}\left(-\frac{1}{2}\right)$
Ex 2.1 Q2 $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$
Ex 2.1 Q3 $\operatorname{cosec}^{-1}(2)$
Ex 2.1 Q4 $\tan^{-1}\left(-\sqrt{3}\right)$
Ex 2.1 Q5 $\cos^{-1}\left(-\frac{1}{2}\right)$
Ex 2.1 Q6 $\tan^{-1}(-1)$
Ex 2.1 Q7 $\sec^{-1}\left(\frac{2}{\sqrt{3}}\right)$
Ex 2.1 Q8 $\cot^{-1}\left(\sqrt{3}\right)$
Ex 2.1 Q9 $\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)$
Ex 2.1 Q10 $\operatorname{cosec}^{-1}\left(-\sqrt{2}\right)$
Ex 2.1 Q11 $\tan^{-1}(1) + \cos^{-1}\left(-\frac{1}{2}\right) + \sin^{-1}\left(-\frac{1}{2}\right)$
Ex 2.1 Q12 $\cos^{-1}\left(\frac{1}{2}\right) + 2\sin^{-1}\left(\frac{1}{2}\right)$
Ex 2.1 Q13 $\sin^{-1} x = y$
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Ex 2.1 Q14 $\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$
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2.3 Properties of Inverse Trigonometric Functions

18 q

Solved Examples

Worked · 3

2.2 Eg.3 $\sin^{-1}\left(2x\sqrt{1-x^2}\right) = 2\sin^{-1} x,\ -\frac{1}{\sqrt{2}} \le x \le \frac{1}{\sqrt{2}}$
2.2 Eg.4 $\tan^{-1}\left(\frac{\cos x}{1-\sin x}\right),\ -\frac{3\pi}{2} < x < \frac{\pi}{2}$
2.2 Eg.5 $\cot^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right),\ x > 1$

Exercise 2.2

Practice · 15

Ex 2.2 Q1 $3\sin^{-1} x = \sin^{-1}\left(3x - 4x^3\right),\ x \in \left[-\frac{1}{2}, \frac{1}{2}\right]$
Ex 2.2 Q2 $3\cos^{-1} x = \cos^{-1}\left(4x^3 - 3x\right),\ x \in \left[\frac{1}{2}, 1\right]$
Ex 2.2 Q3 $\tan^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right),\ x \ne 0$
Ex 2.2 Q4 $\tan^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right),\ 0 < x < \pi$
Ex 2.2 Q5 $\tan^{-1}\left(\frac{\cos x - \sin x}{\cos x + \sin x}\right),\ \frac{-\pi}{4} < x < \frac{3\pi}{4}$
Ex 2.2 Q6 $\tan^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right),\ |x| < a$
Ex 2.2 Q7 $\tan^{-1}\left(\frac{3a^2 x - x^3}{a^3 - 3a x^2}\right),\ a > 0;\ \frac{-a}{\sqrt{3}} < x < \frac{a}{\sqrt{3}}$
Ex 2.2 Q8 $\tan^{-1}\left[2\cos\left(2\sin^{-1}\frac{1}{2}\right)\right]$
Ex 2.2 Q9 $\tan\frac{1}{2}\left[\sin^{-1}\frac{2x}{1+x^2} + \cos^{-1}\frac{1-y^2}{1+y^2}\right],\ |x| < 1,\ y > 0$
Ex 2.2 Q10 $\sin^{-1}\left(\sin\frac{2\pi}{3}\right)$
Ex 2.2 Q11 $\tan^{-1}\left(\tan\frac{3\pi}{4}\right)$
Ex 2.2 Q12 $\tan\left(\sin^{-1}\frac{3}{5} + \cot^{-1}\frac{3}{2}\right)$
Ex 2.2 Q13 $\cos^{-1}\left(\cos\frac{7\pi}{6}\right)$
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Ex 2.2 Q14 $\sin\left(\frac{\pi}{3} - \sin^{-1}\left(-\frac{1}{2}\right)\right)$
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Ex 2.2 Q15 $\tan^{-1}\sqrt{3} - \cot^{-1}\left(-\sqrt{3}\right)$
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Miscellaneous Exercise on Chapter 2

15 q

Solved Examples

Worked · 1

Misc Eg.6 $\sin^{-1}\left(\sin\frac{3\pi}{5}\right)$

Miscellaneous Exercise

Practice · 14

Misc Q1 $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$
Misc Q2 $\tan^{-1}\left(\tan\frac{7\pi}{6}\right)$
Misc Q3 $2\sin^{-1}\frac{3}{5} = \tan^{-1}\frac{24}{7}$
Misc Q4 $\sin^{-1}\frac{8}{17} + \sin^{-1}\frac{3}{5} = \tan^{-1}\frac{77}{36}$
Misc Q5 $\cos^{-1}\frac{4}{5} + \cos^{-1}\frac{12}{13} = \cos^{-1}\frac{33}{65}$
Misc Q6 $\cos^{-1}\frac{12}{13} + \sin^{-1}\frac{3}{5} = \sin^{-1}\frac{56}{65}$
Misc Q7 $\tan^{-1}\frac{63}{16} = \sin^{-1}\frac{5}{13} + \cos^{-1}\frac{3}{5}$
Misc Q8 $\tan^{-1}\sqrt{x} = \frac{1}{2}\cos^{-1}\left(\frac{1-x}{1+x}\right),\ x \in [0, 1]$
Misc Q9 $\cot^{-1}\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right) = \frac{x}{2},\ x \in \left(0, \frac{\pi}{4}\right)$
Misc Q10 $\tan^{-1}\left(\frac{\sqrt{1+x} - \sqrt{1-x}}{\sqrt{1+x} + \sqrt{1-x}}\right) = \frac{\pi}{4} - \frac{1}{2}\cos^{-1} x,\ -\frac{1}{\sqrt{2}} \le x \le 1$
Misc Q11 $2\tan^{-1}(\cos x) = \tan^{-1}(2\operatorname{cosec} x)$
Misc Q12 $\tan^{-1}\frac{1-x}{1+x} = \frac{1}{2}\tan^{-1} x,\ (x > 0)$
Misc Q13 $\sin\left(\tan^{-1} x\right),\ |x| < 1$
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Misc Q14 $\sin^{-1}(1-x) - 2\sin^{-1} x = \frac{\pi}{2}$
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What the board has asked from this chapter

Questions per paper · 21 papers · 2023 to 2026

Bars average the full papers of each year. 33 further questions come from set variants and are listed below.

2026

25 q

1 $f(x) = \cos^{-1} (2x - 5)$
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Domains, Ranges and Principal Value Branches
1 $2 \cos^{-1} x = y$
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Domains, Ranges and Principal Value Branches
1 $The following graph represents :$
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Domains, Ranges and Principal Value Branches
1 $The following graph represents :$
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Domains, Ranges and Principal Value Branches
1 $The following graph represents :$
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Domains, Ranges and Principal Value Branches
3 $For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined ?$
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Domains, Ranges and Principal Value Branches
3 $\sec^{-1}\left(\sqrt{2}\right) + 2\operatorname{cosec}^{-1}\left(-\sqrt{2}\right)$
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Evaluating Inverse Trigonometric Expressions
5 $\cos^{-1} (4x + 1)$
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Domains, Ranges and Principal Value Branches
5 $\sin^{-1} x + \pi = y$
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Domains, Ranges and Principal Value Branches
12 $\tan^{-1} x = 3y$
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Domains, Ranges and Principal Value Branches
12 $\sin^{-1} (1 - 2x)$
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Domains, Ranges and Principal Value Branches
21 $\tan\left[\cos^{-1}\left(\tan \dfrac{3\pi}{4}\right)\right]$
Evaluating Inverse Trigonometric Expressions
21 $\sin\left[\tan^{-1}\tan\left(\dfrac{3\pi}{4}\right)\right]$
Evaluating Inverse Trigonometric Expressions
21 $\sin\left[\cos^{-1}\cos\left(\dfrac{7\pi}{6}\right)\right]$
Evaluating Inverse Trigonometric Expressions
21 $\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right) + \cot^{-1}\left(\dfrac{1}{\sqrt{3}}\right) + \tan^{-1}\left(\sin\left(-\dfrac{\pi}{2}\right)\right) + \tan^{-1}\left(\tan\dfrac{2\pi}{3}\right)$
Evaluating Inverse Trigonometric Expressions
23 (a) $\sin [\cot^{-1} \sqrt{2}\, (\cos (\tan^{-1} 1))]$
Evaluating Inverse Trigonometric Expressions
23 (a) $\sin^{-1} \sqrt{\frac{1 + \cos 2x}{2}}$
Properties of Inverse Trigonometric Functions
25 (a) $\tan^{-1} \left( \frac{\cos 2x - \sin 2x}{\cos 2x + \sin 2x} \right)$
Properties of Inverse Trigonometric Functions
23 (b) $\cos[\sin^{-1}(-1) - \tan^{-1}(-\sqrt{3})]$
Evaluating Inverse Trigonometric Expressions
25 (a) $\cot^{-1} \sqrt{\frac{1 + \cos 2x}{1 - \cos 2x}}$
Properties of Inverse Trigonometric Functions
25 (b) $\tan \left( \sin^{-1} 1 - \cos^{-1} \left( -\frac{1}{2} \right) \right)$
Evaluating Inverse Trigonometric Expressions
25 (b) $\sin \left( \tan^{-1} \left( -\sqrt{3} \right) - \sec^{-1} 2 \right)$
Evaluating Inverse Trigonometric Expressions
32 $p(x) = \sin^{-1}(1 - 2x^2)$
Domains, Ranges and Principal Value Branches
33 $q(x) = \cos^{-1} (4x^2 - 3)$
Domains, Ranges and Principal Value Branches
34 $g(x) = \cos^{-1}(x^2 - 1)$
Domains, Ranges and Principal Value Branches

2025

25 q

1 $\sin^{-1}\left(\sin\left(-\frac{10\pi}{3}\right)\right)$
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Evaluating Inverse Trigonometric Expressions
1 $\cos^{-1} x$
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Domains, Ranges and Principal Value Branches
1 $\sin^{-1}(2x^2 - 3)$
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Domains, Ranges and Principal Value Branches
1 $The given graph illustrates :$
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Domains, Ranges and Principal Value Branches
1 $Study the given graph. It illustrates :$
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Domains, Ranges and Principal Value Branches
2 $f(x) = \cos^{-1} x + \sin x$
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Domains, Ranges and Principal Value Branches
3 $The graph shown below depicts :$
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Domains, Ranges and Principal Value Branches
3 $The graph shown below depicts :$
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Domains, Ranges and Principal Value Branches
3 $The following graph is a combination of :$
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Domains, Ranges and Principal Value Branches
5 $\sin^{-1}\left(\cos \dfrac{43\pi}{5}\right)$
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Evaluating Inverse Trigonometric Expressions
5 $y = \sin^{-1} x$
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Domains, Ranges and Principal Value Branches
5 $\left[ \sec^{-1}(-\sqrt{2}) - \tan^{-1}\left(\dfrac{1}{\sqrt{3}}\right) \right]$
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Evaluating Inverse Trigonometric Expressions
5 $\cos\left(\dfrac{\pi}{6} + \cot^{-1}(-\sqrt{3})\right)$
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Evaluating Inverse Trigonometric Expressions
21 $\sec^{-1}(2x + 1)$
Domains, Ranges and Principal Value Branches
7 $\cot^{-1}\left(-\dfrac{1}{\sqrt{3}}\right)$
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Domains, Ranges and Principal Value Branches
21 $\sin^{-1}(x^2 - 3)$
Domains, Ranges and Principal Value Branches
18 $The graph of a trigonometric function is as shown. Which of the following will represent graph of its inverse ?$
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Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
20 $\sec^{-1}\left(\dfrac{\sqrt{3}}{2}\right)$
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Domains, Ranges and Principal Value Branches
21 $f(x) = \cos^{-1}(x^2 - 4)$
Domains, Ranges and Principal Value Branches
21 $f(x) = \sin^{-1}(-x^2)$
Domains, Ranges and Principal Value Branches
22 $\tan^{-1}\left[2\sin\left(2\cos^{-1}\frac{\sqrt{3}}{2}\right)\right]$
Evaluating Inverse Trigonometric Expressions
23 (a) $\sin^{-1}\left(\frac{x}{\sqrt{1 + x^2}}\right)$
Properties of Inverse Trigonometric Functions
23 (b) $\sin^{-1}\sqrt{x - 1}$
Domains, Ranges and Principal Value Branches
24 $x$
Properties of Inverse Trigonometric Functions
24 $\sin^{-1}\left(\sin \frac{3\pi}{5}\right)$
Evaluating Inverse Trigonometric Expressions

2024

17 q

Direction : In questions numbers 19 and 20, two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the following options :
19 $y = \cos^{-1}(x)$
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Domains, Ranges and Principal Value Branches
21 $= \sin^{-1}\left(\dfrac{\sqrt{2}}{2}\right) + \cos^{-1}\left(-\dfrac{1}{2}\right)$
Evaluating Inverse Trigonometric Expressions
21 $\sin^{-1}\left[\mathrm{k}\tan\left(2\cos^{-1}\dfrac{\sqrt{3}}{2}\right)\right] = \dfrac{\pi}{3}$
Evaluating Inverse Trigonometric Expressions
21 (a) $\tan^{-1}\left(\dfrac{\cos x}{1 - \sin x}\right)$
Properties of Inverse Trigonometric Functions
21 $\cos^{-1}x + \cos^{-1}\left[\dfrac{x}{2} + \dfrac{\sqrt{3 - 3x^2}}{2}\right]$
Properties of Inverse Trigonometric Functions
21 $\sec^2\left(\tan^{-1}\dfrac{1}{2}\right) + \operatorname{cosec}^2\left(\cot^{-1}\dfrac{1}{3}\right)$
Evaluating Inverse Trigonometric Expressions
21 (a) $\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right) + \cot^{-1}\left(\dfrac{1}{\sqrt{3}}\right) + \tan^{-1}\left[\sin\left(-\dfrac{\pi}{2}\right)\right]$
Evaluating Inverse Trigonometric Expressions
22 (a) $\sin^{-1}\left(-\dfrac{1}{2}\right) + \cos^{-1}\left(-\dfrac{\sqrt{3}}{2}\right) + \cot^{-1}\left(\tan \dfrac{4\pi}{3}\right)$
Evaluating Inverse Trigonometric Expressions
21 (b) $f(x) = \sin^{-1}(x^2 - 4)$
Domains, Ranges and Principal Value Branches
21 (b) $\tan^{-1}(1) + \cos^{-1}\left(-\dfrac{1}{2}\right) + \sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$
Domains, Ranges and Principal Value Branches
22 $\cot^2\left\{\operatorname{cosec}^{-1} 3\right\} + \sin^2\left\{\cos^{-1}\left(\dfrac{1}{3}\right)\right\}$
Evaluating Inverse Trigonometric Expressions
22 (b) $f(x) = \cos^{-1}(1 - x^2)$
Domains, Ranges and Principal Value Branches
24 $\left[ \sin^2 \left\{ \cos^{-1}\left(\dfrac{3}{5}\right) \right\} + \tan^2 \left\{ \sec^{-1}(3) \right\} \right]$
Evaluating Inverse Trigonometric Expressions
If a function $f : X \to Y$ defined as $f(x) = y$ is one-one and onto, then we can define a unique function $g : Y \to X$ such that $g(y) = x$ , where $x \in X$ and $y = f(x)$ , $y \in Y$ . Function g is called the inverse of function f. The domain of sine function is R and function sine : $R \to R$ is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to $[-1, 1]$ such that inverse of sine function exists, i.e., $\sin^{-1} x$ is defined from $[-1, 1]$ to A. On the basis of the above information, answer the following questions :
38 (i) $If A is the interval other than principal value branch, give an example of one such interval.$
Domains, Ranges and Principal Value Branches
If a function $f : X \to Y$ defined as $f(x) = y$ is one-one and onto, then we can define a unique function $g : Y \to X$ such that $g(y) = x$ , where $x \in X$ and $y = f(x)$ , $y \in Y$ . Function g is called the inverse of function f. The domain of sine function is R and function sine : $R \to R$ is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to $[-1, 1]$ such that inverse of sine function exists, i.e., $\sin^{-1} x$ is defined from $[-1, 1]$ to A. On the basis of the above information, answer the following questions :
38 (ii) $\sin^{-1} (x)$
Evaluating Inverse Trigonometric Expressions
If a function $f : X \to Y$ defined as $f(x) = y$ is one-one and onto, then we can define a unique function $g : Y \to X$ such that $g(y) = x$ , where $x \in X$ and $y = f(x)$ , $y \in Y$ . Function g is called the inverse of function f. The domain of sine function is R and function sine : $R \to R$ is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to $[-1, 1]$ such that inverse of sine function exists, i.e., $\sin^{-1} x$ is defined from $[-1, 1]$ to A. On the basis of the above information, answer the following questions :
38 (iii) (a) $\sin^{-1} x$
Domains, Ranges and Principal Value Branches
If a function $f : X \to Y$ defined as $f(x) = y$ is one-one and onto, then we can define a unique function $g : Y \to X$ such that $g(y) = x$ , where $x \in X$ and $y = f(x)$ , $y \in Y$ . Function g is called the inverse of function f. The domain of sine function is R and function sine : $R \to R$ is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to $[-1, 1]$ such that inverse of sine function exists, i.e., $\sin^{-1} x$ is defined from $[-1, 1]$ to A. On the basis of the above information, answer the following questions :
38 (iii) (b) $f(x) = 2 \sin^{-1} (1 - x)$
Domains, Ranges and Principal Value Branches

2023

15 q

2 $\sin\left[\dfrac{\pi}{3} + \sin^{-1}\left(\dfrac{1}{2}\right)\right]$
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Evaluating Inverse Trigonometric Expressions
In the following questions 19 & 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices :
19 $(\cos^{-1} x)^2$
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Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.
19 $f(x) = 2 \sin^{-1} x + \frac{3\pi}{2}$
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Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.
19 $\tan^{-1} x$
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Domains, Ranges and Principal Value Branches
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d) as given below.
19 $\left[ \sin^{-1} x + 2 \cos^{-1} x \right]$
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Domains, Ranges and Principal Value Branches
21 $f(x) = \cos^{-1} x$
Domains, Ranges and Principal Value Branches
21 $f(x) = \tan^{-1} x$
Domains, Ranges and Principal Value Branches
21 (a) $y = \sin^{-1}(x^2 - 4)$
Domains, Ranges and Principal Value Branches
21 (a) $\sin^{-1}\left(\sin \frac{3\pi}{4}\right) + \cos^{-1}(\cos \pi) + \tan^{-1}(1)$
Evaluating Inverse Trigonometric Expressions
21 (b) $\cos^{-1}\left[\cos\left(-\dfrac{7\pi}{3}\right)\right]$
Evaluating Inverse Trigonometric Expressions
21 (b) $\sin^{-1}\left(\sin \frac{3\pi}{4}\right) + \cos^{-1}\left(\cos \frac{3\pi}{4}\right) + \tan^{-1}(1)$
Evaluating Inverse Trigonometric Expressions
21 (b) $\cos^{-1} x$
Domains, Ranges and Principal Value Branches
22 $\tan^{-1}\left[2\cos\left(2\sin^{-1}\dfrac{1}{2}\right)\right] + \tan^{-1} 1$
Evaluating Inverse Trigonometric Expressions
24 (a) $3 \sin^{-1} \left( \frac{1}{\sqrt{2}} \right) + 2 \cos^{-1} \left( \frac{\sqrt{3}}{2} \right) + \cos^{-1} (0)$
Evaluating Inverse Trigonometric Expressions
24 (b) $f(x) = \sin^{-1} x$
Domains, Ranges and Principal Value Branches

The 10 board questions to practise first

The questions the board asked again come first, most asked first. Each one says how often and when.

Question 1
Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)
21 $\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right) + \cot^{-1}\left(\dfrac{1}{\sqrt{3}}\right) + \tan^{-1}\left(\sin\left(-\dfrac{\pi}{2}\right)\right) + \tan^{-1}\left(\tan\dfrac{2\pi}{3}\right)$
Question 2
Asked 2 times: 2023*, 2025 (* = numbers or wording changed that year)
22 $\tan^{-1}\left[2\sin\left(2\cos^{-1}\frac{\sqrt{3}}{2}\right)\right]$
Question 3
Asked 2 times: 2023, 2024
21 (b) $f(x) = \sin^{-1}(x^2 - 4)$
Question 4
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026
34 $g(x) = \cos^{-1}(x^2 - 1)$
Question 5
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026
25 (b) $\sin \left( \tan^{-1} \left( -\sqrt{3} \right) - \sec^{-1} 2 \right)$
Question 6
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026
3 $For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined ?$
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Question 7
This type asked 3 times: 2023, 2025, 2026. This one: 2026
21 $\tan\left[\cos^{-1}\left(\tan \dfrac{3\pi}{4}\right)\right]$
Question 8
This type asked 3 times: 2024, 2025, 2026. This one: 2026
25 (a) $\tan^{-1} \left( \frac{\cos 2x - \sin 2x}{\cos 2x + \sin 2x} \right)$
Question 9
This type asked 3 times: 2023, 2024, 2025. This one: 2025
Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
20 $\sec^{-1}\left(\dfrac{\sqrt{3}}{2}\right)$
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Question 10
This type asked 2 times: 2025, 2026. This one: 2026
5 $\cos^{-1} (4x + 1)$
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2.2 Basic Concepts

Solved Examples

Exercise 2.1

2.3 Properties of Inverse Trigonometric Functions

Solved Examples

Exercise 2.2

Miscellaneous Exercise on Chapter 2

Solved Examples

Miscellaneous Exercise

What the board has asked from this chapter

2026

2025

2024

2023

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10