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If f(x)=cos(logx), then value of f(x) f(...

If `f(x)=cos(logx),` then value of `f(x) f(4)-1/2{f(x/4)+f(4x)}` is (a) `1` (b) `-1` (c) `0` (d) `+- 1`

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Given, `f(x) = cos (log x)`
Now,
`f(x)f(4)-1/2{f(x/4)+f(4x)}`
`=cos(logx)cos(log4)-1/2 {cos(log(x/4))+cos{log4x}`
...
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