Question

Evaluate :

$\int \frac{2}{1+\cos 2x}dx$

Answer 1

We know,

$1+\cos 2x=2{\cos }^{2}x$

$I=\int \frac{2}{1+\cos 2x}dx=\int \frac{2}{2{\cos }^{2}x}dx$

$I=\int {\sec }^{2}xdx$

$I=\tan x+C$