Question

Prove 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 = sin3 x - sin x + sin 2x

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

$=2sinx\left(2cos3\frac{x}{2}cos\frac{x}{2}\right)=4sinxcos\frac{x}{2}cos\frac{3x}{2}$