Question:
Prove that
$\frac{\sin 2 x}{1-\cos 2 x}=\cot x$
Solution:
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
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