Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 694: 87

$\sin 4x=4\sin x\cos x\cos 2x$

Start with the left side: $\sin 4x$ Rewrite $\sin 4x$ as $\sin (2*2x)$ and use the double-angle identity: $=\sin (2*2x)$ $=2\sin 2x\cos 2x$ Use the double-angle identity again: $=2(2\sin x\cos x)\cos 2x$ $=4\sin x\cos x\cos 2x$