已知函数f(x)=sinx+sin（x+2/3π)(x∈R )（1）函数y=f(x)的图像的二相邻对

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f(x)=sinx+sin(x+2π/3)
=simx+simxcos2π/3+cosxsin2π/3
=sinx-1/2sinx+√3/2cosx
=1/2sinx+√3/2cosx
=sin(x+π/3)
(1)∵T=2π,∴相邻两个对称轴之间的距离是π；
(2)f(x)=1/3,即sin(x+π/3)=1/3,
∴cos(2x+2π/3)=cos2(x+π/3)=1-2sin²(x+π/3)=1-2/9=7/9
======以下答案可供参考======
供参考答案1:
（1）f(x)=sinx-1/2sinx+√3/2cosx=1/2sinx+√3/2cosx=sin(x+π/3)
∴最小正周期T=2π
∴二相邻对称轴之间的距离：T/2=π
（2）f(x)=sin(x+π/3)=1/3
∴cos(2x+2π/3)=1-2sin²(x+π/3)=1-1/9=8/9
供参考答案2:
（1）f(x)=sinx+sinx*(-1/2)+根号3/2cosx
=1/2sinx+根号3/2cosx
=sin(x+π/3）
则周期为2π，两相邻对称轴之间距离为π
（2）f(x)=sin(x+Pai/3)=1/3
推出cos（2x+2π/3）=1-2（sin(x+π/3））^2=7/9