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CBSE - Class 12 Mathematics Inverse Trigonometric Functions Worksheet

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

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

Write the following functions in the simplest form: $\tan^{-1} (\frac{\cos x - \sin x}{\cos x + \sin x})$, $\frac{-\pi}{4} < x < \frac{3\pi}{4}$

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

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

Write the following functions in the simplest form: $\tan^{-1} \frac{x}{\sqrt{a^2 - x^2}}$, $|x| < a$

Prove that $2\sin^{-1} \frac{3}{5} = \tan^{-1} \frac{24}{7}$

$\sin(\tan^{-1} x)$, $|x| < 1$ 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. $\frac{x}{\sqrt{1+x^2}}$

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

10.

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

11.

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

12.

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

13.

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

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

14.

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

15.

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

16.

Prove that $\cot^{-1} (\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}) = \frac{x}{2}$, $x \in (0, \frac{\pi}{4})$

17.

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

18.

Write the following functions in the simplest form: $\tan^{-1} \frac{\sqrt{1+x^2}-1}{x}$, $x \neq 0$

19.

Find the values of the following: $\cos^{-1}(\frac{1}{2}) + 2\sin^{-1}(\frac{1}{2})$

20.

$\cos^{-1}(\cos(\frac{7\pi}{6}))$ is equal to

a. $\frac{7\pi}{6}$ b. $\frac{5\pi}{6}$ c. $\frac{\pi}{3}$ d. $\frac{\pi}{6}$

Worksheet Answers

13.

20.

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