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

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

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

Options:

$\cot x+c$

$-\cot x+c$

$-\frac{1}{2}\cot x+c$

$\log\cot x+c$

Correct Answer:

$-\frac{1}{2}\cot x+c$

Explanation:

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

$=\int\frac{1}{2\sin^2x}dx$

$=\frac{1}{2}\int cosec^2x\,dx$

$=-\frac{1}{2}\cot x+c$