Question

Show that$\sin 3x+\sin 2x-\sin x=4\sin x\cos \frac{x}{2}\cos \frac{3x}{2}$

Answer 1

$\sin 3x+\sin 2x-\sin x=2\cos 2x\sin x+\sin 2x$

$=2\cos 2x\sin x+2\sin x\cos x$

$=2\sin x(\cos x+\cos 2x)$

$=2\sin x(2\cos \frac{x}{2}\cdot \cos \frac{3x}{2})$

$\sin 3x+\sin 2x-\sin x=4\sin x\cdot \cos \frac{x}{2}\cdot \cos \frac{3x}{2}$.