CBSE - Class 12 Mathematics Inverse Trigonometric Functions Worksheet
1.
Prove that $\tan^{-1}(\frac{\sqrt{1+x} - \sqrt{1-x}}{\sqrt{1+x} + \sqrt{1-x}}) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1} x$, $\frac{-1}{\sqrt{2}} \leq x \leq 1$
2.
Find the values of each of the following: $\tan^{-1} [2\cos(2\sin^{-1}(\frac{1}{2}))]$
3.
Prove that $\sin^{-1} \frac{8}{17} + \sin^{-1} \frac{3}{5} = \tan^{-1} \frac{77}{36}$
4.
Find the principal values of the following: $\cos^{-1} (\frac{-1}{2})$
5.
Find the principal values of the following: $\tan^{-1} (-1)$
6.
$\sin(\frac{\pi}{3} - \sin^{-1}(\frac{-1}{2}))$ is equal to
a.
$\frac{1}{2}$
b.
$\frac{1}{3}$
c.
$\frac{1}{4}$
d.
$1$
7.
Solve the following equations: $2\tan^{-1}(\cos x) = \tan^{-1}(2 \csc x)$
8.
Prove that $\cos^{-1} \frac{12}{13} + \sin^{-1} \frac{3}{5} = \sin^{-1} \frac{56}{65}$
9.
Find the values of each of the expressions: $\sin^{-1}(\sin(\frac{2\pi}{3}))$
10.
Find the values of the following: $\cos^{-1}(\frac{1}{2}) + 2\sin^{-1}(\frac{1}{2})$
11.
Prove that $\cos^{-1} \frac{4}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} \frac{33}{65}$
12.
Write the following functions in the simplest form: $\tan^{-1} \frac{\sqrt{1+x^2}-1}{x}$, $x \neq 0$
13.
Find the principal values of the following: $\cosec^{-1} (-\sqrt{2})$
14.
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 $xy < 1$
15.
Prove that $\tan^{-1} \frac{63}{16} = \sin^{-1} \frac{5}{13} + \cos^{-1} \frac{3}{5}$
16.
Find the values of the following: $\tan^{-1}(1) + \cos^{-1}(\frac{-1}{2}) + \sin^{-1}(\frac{-1}{2})$
17.
Prove the following: $3\cos^{-1} x = \cos^{-1} (4x^3 - 3x)$, $x \in [\frac{1}{2}, 1]$
18.
Find the value of the following: $\cos^{-1}(\cos(\frac{13\pi}{6}))$
19.
Find the principal values of the following: $\cos^{-1} (\frac{-1}{\sqrt{2}})$
20.
Find the principal values of the following: $\tan^{-1} (-\sqrt{3})$
