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  • If f(x)=cos (ln x) , then the value of f(x)f(y)-1/2 [f(xy)+f(x/y)], is

If f(x)=cos (ln x) , then the value of f(x)f(y)-1/2 [f(xy)+f(x/y)], is

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Solution:   We have ,  f(x)=cos (ln x)

                Rightarrow      f(x)f(y)-frac12[f(xy)-f(fracxy)]

               Rightarrow      f(xy)=cos [ln x+ln y]   and

              Rightarrow       f(fracxy)=cos [ln x-ln y]

          Now ,    f(x)f(y)-frac12[f(xy)-f(fracxy)]=0

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Deependra Verma

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