已知sin(x-60°)=2/3,求sin(x+60°)-根号3cos(120°-x)的值

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已知sin(x-60°)=2/3,求sin(x+60°)-根号3cos(120°-x)的值

已知sin(x-60°)=2/3,求sin(x+60°)-根号3cos(120°-x)的值
已知sin(x-60°)=2/3,求sin(x+60°)-根号3cos(120°-x)的值

已知sin(x-60°)=2/3,求sin(x+60°)-根号3cos(120°-x)的值
sin(x+60°)-根号3cos(120°-x)=sinxcos60°+cosxsin60°-根号3(cos120°cosx+sin120°sinx)
=sinx/2+根号3cosx/2-根号3(-cosx/2+根号3sinx/2)
=-sinx+根号3cosx
=-2(sinx/2-根号3cosx/2)=-2sin(x-60°)=-4/3