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

Question

If f(x) = cos (log x), then f(x²)f(y²)-\(\frac{1}{2}\){f(\(\frac{x^2}{y^2}\))+f(x² y²)} has the value

A. -2 

B. -1 

C. 1/2 

D. None of these

Answer 1

Option : (D)

f(x) = cos (log x)

Now,

f(x²)f(y²)-\(\frac{1}{2}\){f(\(\frac{x^2}{y^2}\))+f(x² y²)}

= cos(2 log x) cos(2 log y)-cos(2 log x) cos(2 log y) 

= 0