如何把函数y=(sinx+sin(x-2π/3))化简,

如何把函数y=(sinx+sin(x-2π/3))化简,
如何把函数y=(sinx+sin(x-2π/3))化简,

如何把函数y=(sinx+sin(x-2π/3))化简,
y=(sinx+sin(x-2π/3))=sinx-sinx/2-√3cosx/2
=sinx/2-√3cosx/2
=sin(x-π/3)

y=sinx+sinxcos2π/3+cosxsin2π/3
=sinx-1/2*sinx+√3/2*cosx
=1/2*sinx+√3/2*cosx
=sinxcosπ/3+cosxsinπ/3
=sin(x+π/3)

根据和差化乘积公式
sinx+siny=2sin((x+y)/2)*cos((x-y)/2)得
y=sin(x-pi/3)

sinx-sinx cos(2pi/3)-cosx sin(2pi/3)
=sinx-sinx /2-3^(1/2) cosx /2
=sinx/2-3^(1/2) cosx /2