# How do you prove sin 4 x = 4 sin x cos x – 8sin^3 x cos x?

Jun 13, 2016

As below

#### Explanation:

RHS
$= 4 \sin x \cos x - 8 {\sin}^{3} x \cos x$

$= 4 \sin x \cos x \left(1 - 2 {\sin}^{2} x\right)$

$= 2 \sin 2 x \cos 2 x = \sin 4 x = L H S$