Question

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

Answer 1

\[\int\left( \frac{1 - \cos x}{1 + \cos x} \right) dx\]

`= ∫ ( {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]`

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

\[ = \int\left( \sec^2  \frac{x}{2} - 1 \right) dx\]

\[ = \frac{\tan \frac{x}{2}}{\frac{1}{2}} - x + C\]

\[ = 2 \tan \frac{x}{2} - x + C\]