1.

If `f(x)=cos (logx)`, then `f(x)f(y)-1/2[f(x/y)+f(xy)]=`

Answer» Correct Answer - A
We have, `f(x)=cos (log _(e) x)`
`therefore f(x) f(y)-(1)/(2){f((x)/(y))+f(xy)}"`
`=cos (log x) cos (log y)-(1)/(2){cos log((x)/(y))+cos (log (x y))}`
`=cos (log x) cos (log y)-(1)/(2){cos (log-x log-y)+cos (log x+log y)}`
`=cos (log x) cos (log y)-(1)/(2){2cos (log x) cos(log y)}`
=0


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