If `f(x) = cos(log x)` then `f(x^2)f(y^2)-1/2[f(x^2y^2)+f(x^2/y^2)]` has the value

Explanation

Given, `f (x) = cos (log x)`


` ⇒ f (x^2) = cos (log x^2)
= cos (2 log x) `


` f (y^2) = cos (log y^2) = cos (2 log y)`


`f ( x^2/ y^2 )= cos ( log x^2/y^2 )=cos (log x^2 - log y^2 ) = cos (2 log x – 2 log y)`
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