求证sint+sin(t+2/3派)+sin(t+4/3派)=0

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求证sint+sin(t+2/3派)+sin(t+4/3派)=0

求证sint+sin(t+2/3派)+sin(t+4/3派)=0
求证sint+sin(t+2/3派)+sin(t+4/3派)=0

求证sint+sin(t+2/3派)+sin(t+4/3派)=0
证明:
sint+sin(t+2/3派)+sin(t+4/3派)
=sint+sint*cos(2π/3)+cost*sin(2π/3)+sint*cos(4π/3)+cost*sin(4π/3)
=sint+sint*(-1/2)+cost*(√3/2)+sint*(-1/2)+cost*(-√3/2)
= 0