If f(x) = cos (log x), then f(x)f(y)-1/2{f(x/y)+f(xy)} has the value A. -1 B. 1/2 C. -2 D. None of these

Question

If f(x) = cos (log x), then f(x)f(y)-\(\frac{1}{2}\){f(\(\frac{x}{y}\))+f(xy)} has the value

A. -1 

B. 1/2 

C. -2

D. None of these

Answer 1

Option : (D)

f(x) = cos (log x)

Now,

f(x)f(y)-\(\frac{1}{2}\){f(\(\frac{x}{y}\))+f(xy)}

= cos(log x) cos(log y)-cos(log x) cos(log y) 

= 0