Question

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

Answer 1

To prove: $\frac{\sin 2x}{1+\cos 2x}=\tan x$

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

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

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

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

$=\tan x$

=R. H. S.
Hence proved.