1.

If `f(x)=cos(log x), " then " f(x)*f(y)-(1)/(2)[f((x)/(y))+f(xy)]` has the valueA. -1B. `(1)/(2)`C. -2D. None of these

Answer» Correct Answer - 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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