Q.

If f(x)=cos⁡loge⁡x, then f(x)f(y)−12fxy+f(xy)has value

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a

-1

b

12

c

-2

d

None of these

answer is D.

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Detailed Solution

fx=cos logx ⇒ fxfy-12fxy+fxy =cos logx cos logy -12coslogx -logy+coslogx+logy=coslogx coslogy-122 coslogx coslogy  since COSA+B+COSA-B=2 COS A COS B=0
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If f(x)=cos⁡loge⁡x, then f(x)f(y)−12fxy+f(xy)has value