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int(sin^2x-cos^2x)/(sin^2cos^2x)dxis eq...

`int(sin^2x-cos^2x)/(sin^2cos^2x)dx`is equal to(A) `tanx+cotx+c` (B) `tanx+cose cx+c`(C) `-tanx+cotx+c` (D) `tanx+secx+c`

A

`tanx+cotx+c`

B

`tanx+cose cx+c`

C

`-tanx+cotx+c`

D

`tanx+secx+c`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `int(sin^2x-cos^2x)/(sin^2xcos^2x)dx`
`=int((sin^2x)/(sin^2xcos^2x)-cos^2x/(sin^2cos^2x))dx`
`=int(sec^2x-cosec^2x)dx`
`=tanx+cotx+c`
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