Question:
Prove that:
$\frac{\sin 2 x}{1+\cos 2 x}=\tan x$
Solution:
$\mathrm{LHS}=\frac{\sin 2 x}{1+\cos 2 x}$
$=\frac{2 \sin x \times \cos x}{1+2 \cos ^{2} x-1} \quad\left[\because \sin 2 x=2 \sin x \times \cos x\right.$ and $\left.\cos 2 x=2 \cos ^{2} x-1\right]$
$=\frac{2 \sin x \times \cos x}{2 \cos x \times \cos x}$
$=\frac{\sin x}{\cos x}$
$=\tan x=\mathrm{RHS}$
Hence proved.