Question

Find the value of $\int \frac{1-\cos 2x}{1+\cos 2x}dx$

Answer 1

Now,

$\int \frac{1-\cos 2x}{1+\cos 2x}dx$

$=\int \frac{2{\sin }^{2}x}{2{\cos }^{2}x}dx$ [ Since $1-\cos 2x=2{\sin }^{2}x$ and $1+\cos 2x=2{\cos }^{2}x$]

$=\int {\tan }^{2}xdx$

$=\sec x+c$ [ Where $c$ is integrating constant]