# How do you prove tan(x) = sin(2x)/[1+cos(2x)]?

$\sin 2 x = 2 \sin x . \cos x$
$\left(1 + \cos 2 x\right) = 2 {\cos}^{2} x$
$\frac{\sin 2 x}{1 + \cos 2 x} = \frac{2 \sin x . \cos x}{2 {\cos}^{2} x} = \sin \frac{x}{\cos x} = \tan x .$