Question

If f(x) = cos(Inx), then $f\left(x\right)f\left(y\right)-\frac{1}{2}\left[f\right(\frac{x}{y})+f(xy\left)\right]$ has the value?

• A. $-1$
• B. $\frac{1}{2}$
• C. $-2$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

$f\left(x\right)=cos\left(logx\right)\therefore f\left(x\right)f\left(y\right)-\frac{1}{2}\left[f\right(\frac{x}{y})+f(xy\left)\right]=cos\left(logx\right)cos\left(logy\right)-\frac{1}{2}\left[cos\right(logx-logy)+cos(logx+logy\left)\right]=cos\left(logx\right)cos\left(logy\right)-\frac{1}{2}\left[2cos\right(logx\left)cos\right(logy\left)\right]=0$