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Let f(x) be a real valued function such ...

Let f(x) be a real valued function such that `f(0)=1/2` and f(x+y)=f(x)f(a-y)+f(y)f(a-x),`forall x,y in R`, then for some real a,

A

f(x) is a periodic function

B

f(x) is a constant function

C

`f(x)=1/2`

D

`f(x)=(cosx)/2`

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A, B, C
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