化简sinx+sin(x+2π⼀3)+cos(x+5π⼀6)

2025年03月18日 01:26
有1个网友回答
网友(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