Question

Prove that $\frac{2\tan x}{1+{\tan }^{2}x}=\sin 2x$

Answer 1

$\frac{2\tan x}{1+{\tan }^{2}x}$

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

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

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

Hence proved.