Question

\[\int\sqrt{\frac{1 + \cos 2x}{1 - \cos 2x}} dx\]

Answer 1

\[\int\sqrt{\frac{1 + \cos2x}{1 - \cos2x}}dx\]
\[ = \int\sqrt{\frac{2 \cos^2 x}{2 \sin^2 x}}dx\]
\[ = \int\ \text{cot  x  dx}\]
\[ = \text{ln} \left| \text{sin  x} \right| + C\]