Question

Prove the following identity:
$\frac{\sin 2x}{1-\cos 2x}=\cot x$

Answer 1

To prove: $\frac{\sin 2x}{1-\cos 2x}=\cot x$

L. H. S.
$=\frac{\sin 2x}{1-\cos 2x}$

$=\frac{2\sin x\times \cos x}{2{\sin }^{2}x}\left[\begin{array}{c}\because \sin 2x=2\sin x\cos x\\ \text{and}1-\cos 2x=2{\sin }^{2}x\end{array}\right]$

$=\frac{2\sin x\times \cos x}{2\sin x\times \sin x}$

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

$=\cot x$

=R. H. S.
Hence proved.