已知sinx+siny+sinz=0,cosx+cosy+cosz=0 则cos(x-y)=______ 要详解

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已知sinx+siny+sinz=0,cosx+cosy+cosz=0 则cos(x-y)=______ 要详解

已知sinx+siny+sinz=0,cosx+cosy+cosz=0 则cos(x-y)=______ 要详解
已知sinx+siny+sinz=0,cosx+cosy+cosz=0 则cos(x-y)=______ 要详解

已知sinx+siny+sinz=0,cosx+cosy+cosz=0 则cos(x-y)=______ 要详解
sinx+siny=-sinz
cosx+cosy=-cosz
平方相加
sin²x+cos²x+sin²y+cos²y+2(cosx+cosy+sinxsiny)=sin²z+cos²z
1+1+2cos(x-y)=1
所以cos(x-y)=-1/2

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