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Iff(x)=sin(logx) then f(xy)+f( y x ​ )...

Iff(x)=sin(logx) then f(xy)+f( y x ​ )−2f(x)cos(logy) is equal to

A

0

B

`(1)/(2)`

C

-2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)=cos(logx)`
` therefore f(x)*f(y)-(1)/(2)[f((x)/(y))+f(xy)]`
`=cos(logx)*cos(log y)-(1)/(2) [cos(logx-log y)+cos(logx+log y)]`
`=cos(logx)*cos(log y)-(1)/(2)[(2 cos(logx)*cos(logy)]`
`=cos (logx)*cos(logy)-cos(logx)*cos(logy)=0`
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