已知sinx-siny=-23

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∵sinx-siny=-23
======以下答案可供参考======
供参考答案1:
sinx-siny=-2/3
平方,得到(sinx)^2-2sinxsiny+(siny)^2=4/9------①
cosx-cosy=2/3
平方,得到(cosx)^2-2cosxcosy+(cosy)^2=4/9------②
①+②有2-2cos(x-y)=8/9
2cos(x-y)=10/9
cos(x-y)=5/9
sin(x-y)=tan(x-y)*cos(x-y)=5/9tan(x-y)
cos(x-y)^2+sin(x-y)^2=1
所以结果tan(a-b)=正负2√14/5
A,B是锐角,sina-sinb所以AA-B即tan(a-b)于是tan(a-b)=-2√14/5