对任意实数x,化简sinx+sin(x+2⼀3派)+sin(x+4⼀3派)=?

2025-03-16 09:56:52
推荐回答(2个)
回答1:

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+sin(x+2π/3+π/3)
=sinx+sin(x+π)
=sinx-sinx
=0

回答2:

sinx+sinxcos120+cosxsin120+sinxcos240+cosxsin240
=sinx-1/2sinx+3^1/2/2cosx-1/2sinx-3^1/2/2cosx
=0