Question

Integrate $\int \frac{1-\cos x}{1+\cos x}dx$

Answer 1

Given

Let $I=\int \frac{1-cosx}{1+cosx}dx$

$\int \frac{1-cosx}{1+cosx}dx=\int \frac{2si{n}^2\frac{x}{2}}{2co{s}^2\frac{x}{2}}dx$

$=\int ta{n}^2\frac{x}{2}dx$

$=\int (se{c}^2\frac{x}{2}-1)dx$

$=\int se{c}^2\frac{x}{2}dx-\int 1dx$

$=\frac{ta{n}^2\frac{x}{2}}{\frac{1}{2}}-x+C$

$I=2ta{n}^2\frac{x}{2}-x+C$