# How do you prove (2tanx)/ (1+tan^2 x) = sin 2x?

Sep 18, 2016

#### Explanation:

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

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

= $\frac{2 \sin \frac{x}{\cos} x}{\frac{1}{\cos} ^ 2 x}$

= $\frac{2 \sin x}{\cos} x \times {\cos}^{2} \frac{x}{1}$

= $2 \sin x \cos x$

= $\sin 2 x$