\(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x=\)

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Question

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VITEEE PYP_125Qs150Min125Marks

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Answer 1

Calculation

\(\int \frac{sin^2 x - cos^2 x}{sin^2 x cos^2 x} dx = \int (\frac{sin^2 x}{sin^2 x cos^2 x} - \frac{cos^2 x}{sin^2 x cos^2 x}) dx\)

⇒ \(\int (sec^2x - cosec^2x) dx\)

⇒ tan x + cot x + c

Hence option 1 is correct

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