Question

Integrate : $\int \frac{1}{1-\cos 2x}dx$

Answer 1

$\int \frac{1}{1-\cos \left(2x\right)}dx$

$=\int \frac{1}{1-(1-2{\sin }^2\left(x\right))}dx$

$=\int \frac{1}{2{\sin }^2\left(x\right)}dx$

$=\frac{1}{2}(-\cot \left(x\right))$

$=-\frac{1}{2}\cot \left(x\right)+C$