Prove that

To Prove: $\frac{\sin 2 x}{1+\cos 2 x}=\tan x$

Taking LHS,

$=\frac{\sin 2 x}{1+\cos 2 x}$

$=\frac{2 \sin x \cos x}{1+\cos 2 x}[\because \sin 2 x=2 \sin x \cos x]$

$=\frac{2 \sin x \cos x}{2 \cos ^{2} x}\left[\because 1+\cos 2 x=2 \cos ^{2} x\right]$

$=\frac{\sin x}{\cos x}$

$=\tan \mathrm{x}\left[\because \tan \theta=\frac{\sin \theta}{\cos \theta}\right]$

= RHS

∴ LHS = RHS

Hence Proved