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CBSE - Class 12 Mathematics Inverse Trigonometric Functions Worksheet

Solve the following equations: $2\tan^{-1}(\cos x) = \tan^{-1}(2 \csc x)$

Find the principal values of the following: $\cosec^{-1} (-\sqrt{2})$

Find the values of each of the following: $\tan^{-1} [2\cos(2\sin^{-1}(\frac{1}{2}))]$

Find the value of the following: $\cos^{-1}(\cos(\frac{13\pi}{6}))$

$\tan^{-1}(\sqrt{3}) - \sec^{-1}(-2)$ is equal to

a. $\pi$ b. $\frac{-\pi}{3}$ c. $\frac{\pi}{3}$ d. $\frac{2\pi}{3}$

$\tan^{-1}(\sqrt{3}) - \cot^{-1}(-\sqrt{3})$ is equal to

a. $\pi$ b. $\frac{-\pi}{2}$ c. $0$ d. $2\sqrt{3}$

Solve the following equations: $\tan^{-1} \frac{1-x}{1+x} = \frac{1}{2} \tan^{-1} x, (x > 0)$

Find the principal values of the following: $\csc^{-1} (2)$

Find the values of each of the expressions: $\sin^{-1}(\sin(\frac{2\pi}{3}))$

10.

If $\sin^{-1} x = y$, then

a. $0 \leq y \leq \pi$ b. $\frac{-\pi}{2} \leq y \leq \frac{\pi}{2}$ c. $0 < y < \pi$ d. $\frac{-\pi}{2} < y < \frac{\pi}{2}$

11.

Find the value of the following: $\tan^{-1}(\tan(\frac{7\pi}{6}))$

12.

Find the values of each of the expressions: $\tan^{-1}(\tan(\frac{3\pi}{4}))$

13.

$\sin(\tan^{-1} x)$, $|x| < 1$ is equal to

a. $\frac{x}{\sqrt{1-x^2}}$ b. $\frac{1}{\sqrt{1-x^2}}$ c. $\frac{1}{\sqrt{1+x^2}}$ d. $\frac{x}{\sqrt{1+x^2}}$

14.

Find the values of each of the expressions: $\tan(\sin^{-1}(\frac{3}{5}) + \cot^{-1}(\frac{3}{2}))$

15.

Find the principal values of the following: $\cos^{-1} (\frac{\sqrt{3}}{2})$

16.

Prove the following: $3\sin^{-1} x = \sin^{-1} (3x - 4x^3)$, $x \in [\frac{-1}{2}, \frac{1}{2}]$

17.

$\sin^{-1}(1 - x) - 2\sin^{-1} x = \frac{\pi}{2}$, then $x$ is equal to

a. $0, \frac{1}{2}$ b. $1, \frac{1}{2}$ c. $0$ d. $\frac{1}{2}$

18.

Prove that $\tan^{-1} \frac{63}{16} = \sin^{-1} \frac{5}{13} + \cos^{-1} \frac{3}{5}$

19.

Prove that $\tan^{-1} \sqrt{x} = \frac{1}{2} \cos^{-1} (\frac{1-x}{1+x})$, $x \in [0, 1]$

20.

Write the following functions in the simplest form: $\tan^{-1} (\sqrt{\frac{1-\cos x}{1+\cos x}})$, $0 < x < \pi$

Worksheet Answers

10.

13.

17.

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