Question

Evaluate :

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

• A. $\log \left(\sec x\right)+C$
• B. $\log \left(\tan x\right)+C$
• C. $\log \left(\cos x\right)+C$
• D. $\log \left(\sin x\right)+C$

Answer 1

The correct option is A $\log \left(\sec x\right)+C$

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

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

$I=\int \tan xdx$

$I=\log \left(\sec x\right)+C$