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CBSE - Class 12 > Mathematics > Inverse Trigonometric Functions Worksheets

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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Chapters in CBSE - Class 12 Mathematics

Application of Derivatives Worksheet Application of Integrals Worksheet Continuity and Differentiability Worksheet Determinants Worksheet Differential Equations Worksheet Integrals Worksheet Linear Programming Worksheet Matrices Worksheet Probability Worksheet Relations and Functions Worksheet Three Dimensional Geometry Worksheet Vector Algebra Worksheet

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