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CBSE - Class 11 Mathematics Trigonometric Functions Worksheet

EXERCISE 3.3

Prove the following: $\cos 6x = 32 \cos^6 x - 48\cos^4 x + 18 \cos^2 x - 1$

Prove the following: $\sin (n + 1)x \sin (n + 2)x + \cos (n + 1)x \cos (n + 2)x = \cos x$

Prove the following: $\sin 2x + 2 \sin 4x + \sin 6x = 4 \cos^2 x \sin 4x$

Prove the following: $\cos(\frac{3\pi}{2} + x) \cos(2\pi + x) [\cot(\frac{3\pi}{2} - x) + \cot(2\pi + x)] = 1$

Prove that: $\cot^2 \frac{\pi}{6} + \text{cosec} \frac{5\pi}{6} + 3\tan^2 \frac{\pi}{6} = 6$

Prove the following: $\frac{\sin x + \sin 3x}{\cos x + \cos 3x} = \tan 2x$

Prove that: $2\sin^2 \frac{\pi}{6} + \text{cosec}^2 \frac{7\pi}{6} \cos^2 \frac{\pi}{3} = \frac{3}{2}$

Prove the following: $\frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x$

Prove the following: $\frac{\sin x - \sin 3x}{\sin^2 x - \cos^2 x} = 2\sin x$

10.

Prove the following: $\cos (\frac{\pi}{4} - x) \cos (\frac{\pi}{4} - y) - \sin (\frac{\pi}{4} - x) \sin (\frac{\pi}{4} - y) = \sin (x+y)$

11.

Prove the following: $\cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1$

12.

Prove the following: $\frac{\cos 9x - \cos 5x}{\sin 17x - \sin 3x} = -\frac{\sin 2x}{\cos 10x}$

13.

Prove that: $\sin^2 \frac{\pi}{6} + \cos^2 \frac{\pi}{3} - \tan^2 \frac{\pi}{4} = -\frac{1}{2}$

14.

Prove the following: $\cot 4x (\sin 5x + \sin 3x) = \cot x (\sin 5x - \sin 3x)$

15.

Prove that: $2\sin^2 \frac{3\pi}{4} + 2\cos^2 \frac{\pi}{4} + 2\sec^2 \frac{\pi}{3} = 10$

16.

Prove the following: $\frac{\sin x - \sin y}{\cos x + \cos y} = \tan \frac{x-y}{2}$

17.

Prove the following: $\frac{\sin 5x + \sin 3x}{\cos 5x + \cos 3x} = \tan 4x$

18.

Find the value of: (ii) $\tan 15^{\circ}$

19.

Prove the following: $\cos(\frac{3\pi}{4} + x) - \cos(\frac{3\pi}{4} - x) = -\sqrt{2} \sin x$

20.

Find the value of: (i) $\sin 75^{\circ}$

Worksheet Answers

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