Question

Simplify: $\frac{\sin 2\theta }{1+\cos 2\theta }$

Answer 1

We have: $\frac{\sin 2\theta }{1+\cos 2\theta }$

$=\frac{2\sin \theta \cos \theta }{1+(2{\cos }^2\theta -1)}$

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

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

$=\tan \theta$