对任意实数x,化简sinx+sin(x+2/3派)+sin(x+4/3派）=?

题目

对任意实数x,化简sinx+sin(x+2/3派)+sin(x+4/3派）=?

答案

sinx+sin(x+2π/3)+sin(x+4π/3)=sinx+sin(x+2π/3)+sin(x+2π/3)cos(2π/3)+sin(2π/3)cos(x+2π/3)=sinx+sin(x+2π/3)-(1/2)sin(x+2π/3)+(√3/2)cos(x+2π/3)=sinx+(1/2)sin(x+2π/3)+(√3/2)cos(x+2π/3)=sinx+s...