Question

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

Answer 1

Consider the $L.H.S$

$\Rightarrow \frac{\sin 2A}{1+\cos 2A}$

We know that $\sin 2A=2\sin A\cos A$

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

Substituting the values in the aboe expression, we get

$\Rightarrow \frac{\sin 2A}{1+\cos 2A}=\frac{2\sin A\cos A}{2{\cos }^{2}A}$

$\Rightarrow \frac{\sin 2A}{1+\cos 2A}=\frac{\sin A}{cosA}$

$\Rightarrow \frac{\sin 2A}{1+\cos 2A}=\tan A=R.H.S$

Therefore, $L.H.S=R.H.S$

Hence Proved.