Question

$\frac{sin2x}{1+cos2x}=tanx$

Answer 1

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

Taking L.H.S.

$\frac{\sin 2x}{1+\cos 2x}$

Using trigonometric identity:

$\sin 2x=2\sin x\cos x$

$\cos 2x=2{\cos }^{2}x-1\Rightarrow 1+\cos 2x=2{\cos }^{2}x$

Therefore,

$\frac{\sin 2x}{1+\cos 2x}$

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

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

$=\tan x$

$=$R.H.S.

Hence proved that $\frac{\sin 2x}{1+\cos 2x}=\tan x$.