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If f(x)sinx.cosxdx=(1)/(2(b^(2)-a^(2)))l...

If `f(x)sinx.cosxdx=(1)/(2(b^(2)-a^(2)))logf(x)+c`, where c is the constant of integration, then `f(x)=`

A

`(2)/((b^(2)-a^(2))cos2x)`

B

`(2)/(abcos2x)`

C

`(2)/((b^(2)-a^(2))sin2x)`

D

`(2)/("ab"sin2x)`

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A
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