Question

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

Answer 1

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

$=\int \frac{2{\sin }^2\frac{x}{2}}{2{\cos }^2\frac{x}{2}}$

$=\int {\tan }^2\frac{x}{2}$

$=\int ({\sec }^2\frac{x}{2}-1)dx=\frac{\tan \frac{x}{2}}{\frac{1}{2}}-x+C$

$=2\tan \frac{x}{2}-x+C$