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Lecture - 10 Chapter 3 Trigonometric Functions

Chapter 3 Miscellaneous Exercise Question 1 $2 \cos \frac{\pi}{13} \cos \frac{9\pi}{13} + \cos \frac{3\pi}{13}\cos \frac{5\pi}{13} = 0$

Question 2 $(\sin 3x + \sin x) \sin x + (\cos 3x – \cos x) \cos x = 0$

Question 3 $(\cos x + \cos y)^2 + (\sin x – \sin y)^2 = 4 \cos^2 \frac{x+y}{2}$

Question 4 $(\cos x – \cos y)^2 + (\sin x – \sin y)^2 = 4 \sin^2 \frac{x-y}{2}$

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

Question 6 $\frac{(\sin 7x + \sin 5x) + (\sin 9x + \sin 3x)}{(\cos 7x + \cos 5x) + (\cos 9x + \cos 3x)} = \tan 6x$

Question 7 $\sin 3x + \sin 2x – \sin x = 4\sin x \cos \frac{x}{2} \cos \frac{3x}{2}$

Example 25 If $\sin x = \frac{3}{5}, \cos y = \frac{-12}{13}$ , where x and y both lie in second quadrant, find the value of $\sin (x+y)$

Example 26 Prove that
$\cos 2x \cos \frac{x}{2} – \cos 3x \cos \frac{9x}{2} = \sin 5x \sin \frac{5x}{2}$