Prove that

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

Taking LHS,

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

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

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

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

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

= RHS

∴ LHS = RHS

Hence Proved