A) \[-1\]
B) \[\frac{1}{2}\]
C) \[-2\]
D) zero
Correct Answer: D
Solution :
Given\[f(x)=\cos (\log x)\] \[\therefore \] \[f(x).f(y)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]\] \[=\cos (\log x).\cos (\log y)\] \[-\frac{1}{2}\left[ \cos \log \left( \frac{x}{y} \right)+\cos \log (xy) \right]\] \[=\cos (\log x)\cos (\log y)-\frac{1}{2}2[\cos (\log x)\] \[\times \cos (\log y)]\] \[=\cos (\log x)\cos (\log y)\] \[-\cos (\log x)\cos (\log y)\] \[=0\] \[\therefore \]\[f(x).f(y)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]=0\]You need to login to perform this action.
You will be redirected in
3 sec