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((cos+sinx))/((1-sin2x))dx=?...

`((cos+sinx))/((1-sin2x))dx=?`

A

`log|sinx-cosx|+C`

B

`(1)/((cosx-sinx))+C`

C

`log|cosx+sinx|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int((cosx+sinx))/((cos^(2)x+sin^(2)-2sinxcosx))dx`.
`=int((cosx+sinx))/((sinx-cosx)^(2))dx=int(1)/(t^(2))dt`, where (sinx-cosx)=t
`=(-1)/(t)+C=(-1)/((sinx-cosx))+C=(1)/((cosx-sinx))+C`.
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