sinx+siny=-1/3 cosx+cosy=1/2,求sin(x+y)的值.

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sinx+siny=-1/3cosx+cosy=1/2,求sin(x+y)的值.sinx+siny=-1/3cosx+cosy=1/2,求sin(x+y)的值.sinx+siny=-1/3cosx+c

sinx+siny=-1/3 cosx+cosy=1/2,求sin(x+y)的值.
sinx+siny=-1/3 cosx+cosy=1/2,求sin(x+y)的值.

sinx+siny=-1/3 cosx+cosy=1/2,求sin(x+y)的值.
sinx+siny=2sin(x/2+y/2)·cos(x/2-y/2)=-1/3----①
cosx+cosy=2cos(x/2+y/2)·cos(x/2-y/2)=1/2----②
①/②=tan(x/2+y/2)=-2/3
根据万能公式：sinα=[2tan(α/2)]/{1+[tan(α/2)]²}
sin(x+y)=(-4/3)/(1+4/9)=-12/13

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