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int(1)/(sin^(2)xcos^(2)x)dx=?...

`int(1)/(sin^(2)xcos^(2)x)dx=?`

A

`tanx+cotx+C`

B

`tanx-cotx+C`

C

`-tanx+cotx+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=it((sin^(2)x+cos^(2)x))/(sin^(2)xcos^(2)x)dx=int(sin^(2)x)/(sin^(2)xcos^(2)x)dx+int(cos^(2)x)/(sin^(2)xcos^(2)x)dx`.
`=int(1)/(cos^(2)x)dx+int(1)/(sin^(2)x)dx=intsec^(2)xdx+int"cosec"^(2)xdx=tanx-cotx+C`.
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