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

CUET Preparation Today

Start Free Mocks

Home Questions PS9U3778FA

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

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

Options:

$\log|\cos x|+c$

$-\log|\cos x|+c$

$-\log|\sec x|+c$

$\log|\cos 2x|+c$

Correct Answer:

$-\log|\cos x|+c$

Explanation:

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

$=\int\tan x\,dx$

$=-\log|\cos x|+c$