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Evaluate: (i) int(cos2x+2\ sin^2x)/(sin^...

Evaluate: (i) `int(cos2x+2\ sin^2x)/(sin^2x)\ dx` (ii) `int(2\ cos^2x-cos2x)/(cos^2x)\ dx`

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(i) `int(frac{cos 2 x+2 sin ^{2} x}{sin ^{2} x}) d x `
`=int(frac{1-2 sin ^{2} x+2 sin ^{2} x}{sin ^{2} x}) d x[because cos 2 x=1-2 sin ^{2} x] `
`=int cosec^{2} x dx `
`=-cot x+C`

ii) `int(frac{2 cos ^{2} x-cos 2 x}{cos ^{2} x}) d x `
`=int(frac{2 cos ^{2} x-(2 cos ^{2} x-1)}{cos ^{2} x}) d x[because cos 2 x=2 cos ^{2} x-1] `
...
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