Question

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

Answer 1

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

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

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

$=\frac{1}{2}\int {\sec }^{2}xdx$

$=\frac{1}{2}\tan x$