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