已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值

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已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(

已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值

已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值
令y=0则2f(x)= 2f(x)f(0) 所以f(0)= 1,然后令x=π/2,y=π/2,所以f(π)+f(0)=2f(π/2)f(π/2)=0,所以f(π)=-1,然后令x=y=π,则f(2π)+f(0)=2f(π)f(π),所以f(2π)=1