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`int(1)/(sin^(2)x.cos^(2)x)dx` is equal to

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`int(1)/(sin^(2)x.cos^(2)x)dx` is equal to
A. `sinx - cos x +C`
B. `tanx +cot x+C`
C. `cos x +sinx +C`
D. `tanx -cot x +C`
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1 Answer

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Correct Answer - D
`int(1)/(sin^(2)xcos^(2)x)dx=int(sin^(2)x+cos^(2)x)/(sin^(2)xcos^(2)x)dx`
`=int((1)/(cos^(2)x)+(1)/(sin^(2)x))dx`
`=int(sec^(2)x+"cosec"^(2)x)dx=tanx-cot x+C`
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