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Free CBSE - Class 12 Mathematics - Inverse Trigonometric Functions worksheets

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Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.
Find the values of each of the following: $\tan^{-1} [2\cos(2\sin^{-1}(\frac{1}{2}))]$
2.
Prove that $\cos^{-1} \frac{4}{5} + \cos^{-1} \frac{12}{13} = \cos^{-1} \frac{33}{65}$
3.
Prove that $\cos^{-1} \frac{12}{13} + \sin^{-1} \frac{3}{5} = \sin^{-1} \frac{56}{65}$
4.
Prove that $\tan^{-1} \frac{63}{16} = \sin^{-1} \frac{5}{13} + \cos^{-1} \frac{3}{5}$
5.
Prove that $\tan^{-1} \sqrt{x} = \frac{1}{2} \cos^{-1} (\frac{1-x}{1+x})$, $x \in [0, 1]$
6.
Prove that $\cot^{-1} (\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}) = \frac{x}{2}$, $x \in (0, \frac{\pi}{4})$
7.
Prove that $\tan^{-1}(\frac{\sqrt{1+x} - \sqrt{1-x}}{\sqrt{1+x} + \sqrt{1-x}}) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1} x$, $\frac{-1}{\sqrt{2}} \leq x \leq 1$
8.
Solve the following equations: $2\tan^{-1}(\cos x) = \tan^{-1}(2 \csc x)$
9.
Solve the following equations: $\tan^{-1} \frac{1-x}{1+x} = \frac{1}{2} \tan^{-1} x, (x > 0)$
10.
$\sin(\tan^{-1} x)$, $|x| < 1$ is equal to
1. $\frac{x}{\sqrt{1-x^2}}$ 2. $\frac{1}{\sqrt{1-x^2}}$ 3. $\frac{1}{\sqrt{1+x^2}}$ 4. $\frac{x}{\sqrt{1+x^2}}$
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