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CBSE - Class 11 Mathematics Trigonometric Functions Worksheet

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

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

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

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

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

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

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 that: $\sin x + \sin 3x + \sin 5x + \sin 7x = 4 \cos x \cos 2x \sin 4x$

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

10.

If in two circles, arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre, find the ratio of their radii.

11.

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

12.

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 $\pi = \frac{22}{7}$).

13.

Find the values of the trigonometric functions: $\sin (-\frac{11\pi}{3})$

14.

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

15.

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

16.

Find the radian measures corresponding to the following degree measures: (iii) $240^{\circ}$

17.

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

18.

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

19.

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

20.

Find the radian measures corresponding to the following degree measures: (ii) $- 47^{\circ}30'$

Worksheet Answers

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