# How do you prove (2tantheta)/(1+tan^2theta)=sin2theta?

Sep 18, 2016

#### Explanation:

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

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

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

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

= $2 \sin \theta \cos \theta$

= $\sin 2 \theta$