Question

Evaluate : ∫ 2/(1-cos2x) dx

\(\int\frac{2}{1-cos\,2x}\)dx

Answer 1

Given,

∫ 2/(1-cos2x) dx

We Know that, 

cos2x = 1 - 2sin²x 

⇒ 1 - cos2x=2sin²x 

Substitute this in the given,

= \(\int\frac{2}{2sin^2x}\) dx

= \(\int\frac{1}{sin^2x}\) dx

= ∫cosec²x dx 

= - cot x + c