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If f (x) = cos ( log e x ) then ...

If f (x) `= cos ( log _e x ) ` then
` f(x) . f(y) - (1)/(2) [f(y/x ) + f (xy)]` has the value

A

-1

B

`1//2`

C

-2

D

0

Text Solution

Verified by Experts

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