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)
问题描述：
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)
答
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