## Precalculus (6th Edition)

$2\cos^2 \frac{x}{2}\tan x=\tan x+\sin x$
Start with the left side: $2\cos^2 \frac{x}{2}\tan x$ Use the half-angle identity for cosine: $=2\left(\pm\sqrt{\frac{1+\cos x}{2}}\right)^2\tan x$ Simplify: $=2*\frac{1+\cos x}{2}*\tan x$ $=(1+\cos x)\tan x$ $=\tan x+\cos x\tan x$ $=\tan x+\cos x*\frac{\sin x}{\cos x}$ $=\tan x+\sin x$ Since this equals the right side, the identity has been proven.