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Evaluate: int(cos2x)/(sin^2x cos^2x)\ dx...

Evaluate: `int(cos2x)/(sin^2x cos^2x)\ dx`

Text Solution

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Solution:
So,
`\int \frac{\cos ^{2} x-\sin ^{2} x}{\sin ^{2} x \cos ^{2} x} d x`
=`\int \frac{\cos ^{2} x d x}{\sin ^{2} x \cos ^{2} x}-\int \frac{\sin ^{2} x}{\sin ^{2} x \cos ^{2}}`
=`\int {cosec}^{2} x d x-\int \sec ^{2} x d x`
=`-cot x-tan x + c`
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