Question

integrate dx/sin^2 x cos^2 x

Answer 1

Hey your answer is -2cot2x +C

Answer 2

Answer :

Now, sin²x cos²x

= 1/4 (4 sin²x cos²x)

= 1/4 (2 sinx cosx)²

= 1/4 (sin2x)²

= 1/4 sin²2x

Now, ∫ dx/(sin²x cos²x)

= 4 ∫ dx/sin²2x

= 4 ∫ cosec²2x dx

= - 4 ∫ (- cosec²2x) dx

= -4/2 ∫ d (cot2x)

= - 2 cot2x + c, where c is integral constant

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