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Evaluate int(cosx-sinx)/(cosx+sinx)(2+2...

Evaluate `int(cosx-sinx)/(cosx+sinx)(2+2sin2x)dx`

Text Solution

Verified by Experts

The correct Answer is:
`sin2x+C`
`int(cosx-sinx)/(cosx+sinx)(2+2sin2x)dx`
`=2int((cosx-sinx)(cosx+sinx)^(2))/(cosx+sinx)dx`
`=2int(cosx-sinx)(cosx+sinx)dx`
`=2int(cos^(2)x-sin^(2)x)dx`
`=2int cos2xdx`
`=sin2x+C`
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