Question

Evaluate:  \[\int\frac{2}{1 - \cos2x}\text{ dx }\]

Answer 1

\[\int\frac{2}{1 - \cos2x}dx = \int\frac{2}{2 \sin^2 x}dx\]
\[ = \int {cosec}^2 \text{ x dx }\]
\[ = - \cot x + c\]
\[\text{ Hence, } \int\frac{2}{1 - \cos2x}dx = - \cot x + c .\]