Question:
Prove that:
$\frac{\sin 2 x}{1-\cos 2 x}=\cot x$
Solution:
LHS $=\frac{\sin 2 x}{1-\cos 2 x}$
$=\frac{2 \sin x \times \cos x}{2 \sin ^{2} x} \quad\left(\because \sin 2 x, 1-\cos 2 x=2 \sin ^{2} x\right)$
$=\frac{2 \sin x \times \cos x}{2 \sin x \times \sin x}$
$=\frac{\cos x}{\sin x}$
$=\cot x=\mathrm{RHS}$
Hence proved.
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