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CBSE - Class 11 Mathematics Trigonometric Functions Worksheet

Find $\sin \frac{x}{2}$, $\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in each of the following : $\cos x = -\frac{1}{3}$, $x$ in quadrant III

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use $\pi = \frac{22}{7}$).

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (ii) 15 cm

Prove the following: $\cos 4x = 1 - 8\sin^2 x \cos^2 x$

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

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

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm

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

Find the values of other five trigonometric functions if $\tan x = -\frac{5}{12}$, $x$ lies in second quadrant.

10.

Prove that: $(\sin 3x + \sin x) \sin x + (\cos 3x - \cos x) \cos x = 0$

11.

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

12.

Prove the following: $\sin^2 6x - \sin^2 4x = \sin 2x \sin 10x$

13.

Prove that: $(\cos x + \cos y)^2 + (\sin x - \sin y)^2 = 4 \cos^2 \frac{x+y}{2}$

14.

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

15.

Prove that: $(\cos x - \cos y)^2 + (\sin x - \sin y)^2 = 4 \sin^2 \frac{x-y}{2}$

16.

Find the values of other five trigonometric functions if $\sec x = \frac{13}{5}$, $x$ lies in fourth quadrant.

17.

Prove the following: $\cos^2 2x - \cos^2 6x = \sin 4x \sin 8x$

18.

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

19.

Find the radian measures corresponding to the following degree measures: (iv) $520^{\circ}$

20.

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

Worksheet Answers

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