Question

已知f(x)满足f(x+y)+f(x-y)=2f(x)*f(y)且f(0)≠2,若f(π/2)=0,求f(π)及f(2π

Answer 1

f(x+y)+f(x-y)=2f(x)*f(y)

x=y=0

f(0)+f(0) =2[f(0)]^2

f(0)=0

x=y=π/2

f(π)+f(0)=2f(π/2).f(π/2)

f(π)=0

x=y =π

f(2π)+f(0)=2f(π)*f(π)

f(2π) = 0