If the function $f(x)=\cos (\log x)$, then the value of $f\left(x^2\right) f\left(y^2\right)-\frac{1

Question

If the function $f(x)=\cos (\log x)$, then the value of $f\left(x^2\right) f\left(y^2\right)-\frac{1}{2}\left[f\left(\frac{x^2}{y^2}\right)+f\left(x^2 y^2\right)\right]$ is

Professor PC Thomas Classes · Answer

Applying logarithmic identities to cosine expansion yields the functional equation zero property.