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Trigonometric Functions EXERCISE 3.3 Solutions
- Q1: Prove that: $\sin^2 \frac{\pi}{6} + \cos^2 \frac{\pi}{3} - \tan^2 \frac{\pi}{4} = -\frac{1}{2}$
- Q2: Prove that: $2\sin^2 \frac{\pi}{6} + \text{cosec}^2 \frac{7\pi}{6} \cos^2 \frac{\pi}{3} = \frac{3}{2}$
- Q3: Prove that: $\cot^2 \frac{\pi}{6} + \text{cosec} \frac{5\pi}{6} + 3\tan^2 \frac{\pi}{6} = 6$
- Q4: Prove that: $2\sin^2 \frac{3\pi}{4} + 2\cos^2 \frac{\pi}{4} + 2\sec^2 \frac{\pi}{3} = 10$
- Q5(i): Find the value of: (i) $\sin 75^{\circ}$
- Q5(ii): Find the value of: (ii) $\tan 15^{\circ}$
- Q6: Prove the following: $\cos (\frac{\pi}{4} - x) \cos (\frac{\pi}{4} - y) - \sin (\frac{\pi}{4} - x) \sin (\frac{\pi}{4} - y) = \sin (x+y)$
- Q7: Prove the following: $\frac{\tan(\frac{\pi}{4} + x)}{\tan(\frac{\pi}{4} - x)} = (\frac{1+\tan x}{1-\tan x})^2$
- Q8: Prove the following: $\frac{\cos(\pi + x) \cos(-x)}{\sin(\pi - x) \cos(\frac{\pi}{2} + x)} = \cot^2 x$
- Q9: Prove the following: $\cos(\frac{3\pi}{2} + x) \cos(2\pi + x) [\cot(\frac{3\pi}{2} - x) + \cot(2\pi + x)] = 1$
- Q10: Prove the following: $\sin (n + 1)x \sin (n + 2)x + \cos (n + 1)x \cos (n + 2)x = \cos x$
- Q11: Prove the following: $\cos(\frac{3\pi}{4} + x) - \cos(\frac{3\pi}{4} - x) = -\sqrt{2} \sin x$
- Q12: Prove the following: $\sin^2 6x - \sin^2 4x = \sin 2x \sin 10x$
- Q13: Prove the following: $\cos^2 2x - \cos^2 6x = \sin 4x \sin 8x$
- Q14: Prove the following: $\sin 2x + 2 \sin 4x + \sin 6x = 4 \cos^2 x \sin 4x$
- Q15: Prove the following: $\cot 4x (\sin 5x + \sin 3x) = \cot x (\sin 5x - \sin 3x)$
- Q16: Prove the following: $\frac{\cos 9x - \cos 5x}{\sin 17x - \sin 3x} = -\frac{\sin 2x}{\cos 10x}$
- Q17: Prove the following: $\frac{\sin 5x + \sin 3x}{\cos 5x + \cos 3x} = \tan 4x$
- Q18: Prove the following: $\frac{\sin x - \sin y}{\cos x + \cos y} = \tan \frac{x-y}{2}$
- Q19: Prove the following: $\frac{\sin x + \sin 3x}{\cos x + \cos 3x} = \tan 2x$
- Q20: Prove the following: $\frac{\sin x - \sin 3x}{\sin^2 x - \cos^2 x} = 2\sin x$
- Q21: Prove the following: $\frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x$
- Q22: Prove the following: $\cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1$
- Q23: Prove the following: $\tan 4x = \frac{4\tan x (1 - \tan^2 x)}{1 - 6\tan^2 x + \tan^4 x}$
- Q24: Prove the following: $\cos 4x = 1 - 8\sin^2 x \cos^2 x$
- Q25: Prove the following: $\cos 6x = 32 \cos^6 x - 48\cos^4 x + 18 \cos^2 x - 1$
Other Exercises for CBSE - Class 11 Mathematics Trigonometric Functions
Chapters in CBSE - Class 11 Mathematics
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