FunctionHard
Question
If f(x) = cos (log x ), then f(x).f(y) 
has the value
has the value Options
A.-1
B.
C.-2
D.None of these
Solution
Given, f (x) = cos (log x)
∴ f(x).f(y)
= cos (log x ). cos (log y )-
[cos(log x - log y) + cos (log x + log y)]
= cos (log x ). cos (log y ) - [(2 cos (log x). cos (log y)]
= cos (log x ). cos (log y ) - cos (log y) - cos (log x). cos (log y) = 0
∴ f(x).f(y)
= cos (log x ). cos (log y )-
[cos(log x - log y) + cos (log x + log y)]= cos (log x ). cos (log y ) -
[(2 cos (log x). cos (log y)] = cos (log x ). cos (log y ) - cos (log y) - cos (log x). cos (log y) = 0
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