y=sinx/2+√3cosx/2是怎么变成2sin(x/2+π/3)的?多于4步.

函数f(x)=sinx/2+αcosx/2的图像关于直线x=π/3对称
∴ x=0和x=2π/3所对应的函数值相等
即 f(0)=f(2π/3)
∴ sin0+αcos0=sin(π/3)+αcos(π/3)
∴ 0+α=√3/2+α*(1/2)
∴ (1/2)α=√3/2
∴ α=√3
即常数α的值等于√3

sin(x/2)+√3cos(x/2)
=2*[1/2*sin(x/2)+√3/2*cos(x/2)]
=2[sin(x/2)cosπ/3+cos(x/2)sinπ/3]
=2sin(x/2+π/3)