CBSE - Class 12 Mathematics Inverse Trigonometric Functions Worksheet
1.
$\cos^{-1}(\cos(\frac{7\pi}{6}))$ is equal to
a.
$\frac{7\pi}{6}$
b.
$\frac{5\pi}{6}$
c.
$\frac{\pi}{3}$
d.
$\frac{\pi}{6}$
2.
Prove that $\tan^{-1}(\frac{\sqrt{1+x} - \sqrt{1-x}}{\sqrt{1+x} + \sqrt{1-x}}) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1} x$, $\frac{-1}{\sqrt{2}} \leq x \leq 1$
3.
Find the principal values of the following: $\cos^{-1} (\frac{-1}{\sqrt{2}})$
4.
Find the principal values of the following: $\tan^{-1} (-\sqrt{3})$
5.
Find the values of each of the expressions: $\tan(\sin^{-1}(\frac{3}{5}) + \cot^{-1}(\frac{3}{2}))$
6.
Find the principal values of the following: $\cot^{-1} (\sqrt{3})$
7.
Find the principal values of the following: $\cos^{-1} (\frac{-1}{2})$
8.
Find the values of each of the following: $\tan \frac{1}{2}[\sin^{-1} \frac{2x}{1+x^2} + \cos^{-1} \frac{1-y^2}{1+y^2}]$, $|x| < 1$, $y > 0$ and $xy < 1$
9.
Find the principal values of the following: $\sec^{-1} (\frac{2}{\sqrt{3}})$
10.
Find the principal values of the following: $\tan^{-1} (-1)$
11.
Prove that $\cos^{-1} \frac{4}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} \frac{33}{65}$
12.
Find the values of each of the following: $\tan^{-1} [2\cos(2\sin^{-1}(\frac{1}{2}))]$
13.
Solve the following equations: $2\tan^{-1}(\cos x) = \tan^{-1}(2 \csc x)$
14.
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.
$\frac{-\pi}{2} < y < \frac{\pi}{2}$
15.
Solve the following equations: $\tan^{-1} \frac{1-x}{1+x} = \frac{1}{2} \tan^{-1} x, (x > 0)$
16.
$\tan^{-1}(\sqrt{3}) - \cot^{-1}(-\sqrt{3})$ is equal to
a.
$\pi$
b.
$\frac{-\pi}{2}$
c.
$0$
d.
$2\sqrt{3}$
17.
Find the principal values of the following: $\sin^{-1} (\frac{-1}{2})$
