Question

Evaluate: $\int \frac{2}{1-\cos 2x}\mathrm{d}x$

Answer 1

$$\begin{gathered} \int \frac{2}{1-\cos 2x}\mathrm{d}x=\int \frac{2}{2{\sin }^{2}x}\mathrm{d}x \\ =\int {\mathrm{cosec}}^{2}x\mathrm{d}x \\ =-\cot x+c \\ \mathrm{Hence},\int \frac{2}{1-\cos 2x}\mathrm{d}x=-\cot x+c. \end{gathered}$$