Evaluate : `int_0^(pi/4)(tanx+cotx)^(-2)dx`

Explanation

`int_{0}^{pi/4}(tan x+cot x)^{-2} d x`
`
=int_{0}^ frac pi/4[frac{sin x}{cos x}+frac{cos x}{sin x}]^{-2}`
`
=int_{0}^{pi/4}[frac{sin ^{2} x+cos x}{cos x sin x}]^{-2}`
`
=int_{0}^{frac pi/4}(cos x sin x)^{2}`
`
=frac{1}{4}[int_{0}^{frac{pi/4}} sin 22 x. `
`
=frac{1}{4}[int_{0}^{frac{pi/4}} frac{1-cos 4 x}{2}]`
`
=frac{1}{8}[x-frac{sin 4 x}{4}]`
`
=frac{1}{8}[frac{pi/4}]`
`
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