设函数F(X)的定义域为R,对任意实数X1,X2,有F(X1)+F(X2)=2F(X1+X2/2)乘以F(X1-X2)/

1.求F(0)的值
F(x1)+F(x2)=2F((x1+x2)/2) F((x1-x2)/2),
x1=x2=x
2F(x)=2F(x)F(0)
F(0)=1
F(x)+F(-x)=2F((x-x)/2) F((x+x)/2)=2F(0)F(x)=2F(x),
F(-x)= F(x)
F(π)+F(0)=2F(π/2)F(π/2)=-1+1=0
F(π/2)=0
F(π-x)+F(x)=2F(π/2)F((π-2x)/2)=0
F(π-x)=-F(x)