Evaluate: `intsqrt((1-cosx)/(1+cosx))dx`

Explanation

We have given

`int sqrt{frac{1+cos x}{1-cos x}} d x`

`I=frac{|cot (frac{x}{2})|}{cot (frac{x}{2})} ln |sin (frac{x}{2})|+C`

As we know that

`1-cos x=2 sin ^{2}(frac{x}{2}) `

`1+cos x=2 cos ^{2}(frac{x}{2})`

Then

`int sqrt{frac{1+cos x}{1-cos x}} d x`

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