Question

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

Answer 1

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

` ∫   \sqrt {{2 sin^2  x/2} / {2 cos^2   x/2 }}      dx`  `[ ∵ 1 - cos x = 2 sin^2      x/2    & 1 + cos x = 2 cos ^2   x/2]`

\[ = \int\tan\frac{x}{2} dx\]

\[ =\text{ - 2 }\text{ln }\left| \cos\frac{x}{2} \right| + C\]