Prove that:


Prove that:

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


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

$=\frac{2 \sin x \times \cos x}{1+2 \cos ^{2} x-1} \quad\left[\because \sin 2 x=2 \sin x \times \cos x\right.$ and $\left.\cos 2 x=2 \cos ^{2} x-1\right]$

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

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

$=\tan x=\mathrm{RHS}$

Hence proved.

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