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int(cos2x)/(sin^2xcos^2x)dx...

`int(cos2x)/(sin^2xcos^2x)dx`

A

`cotx+tanx+C`

B

`-cotx+tanx+C`

C

`cotx-tanx+C`

D

`-cotx-tanx+C`

Text Solution

Verified by Experts

The correct Answer is:
D
`I=int((cos^(2)x-sin^(2)x))/(cos^(2)xsin^(2)x)dx=int(cos^(2)x)/(cos^(2)xsin^(2)x)dx-int(sin^(2)x)/(cos^(2)xsin^(2)x)dx`.
`=int(dx)/(sin^(2)x)-int(dx)/(cos^(2)x)=intcosec^(2)xdx-intsec^(2)xdx`
`=-cotx-tanx+C`.
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