作业帮已知sinx+siny=-0.5,cosx-cosy=0.5,且X.Y都是锐角,则tan(x-y)=
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已知sinx+siny=-0.5,cosx-cosy=0.5,且X.Y都是锐角,则tan(x-y)=
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tan(x-y)=(tanx-tany)/(1+tanx*tany)
=[(sinxcosy-cosxsinx)/(cosxcosy) / [(cosxcosy+sinxsiny)/(cosxcosy)]
=(sinxcosy-cosxsinx)/(cosxcosy+sinxsiny)
=sin(x-y)/cos(x-y)
(sinx+siny)²=0.25
sin²x+sin²y+2sinxsiny =0.25 ①
(cosx-cosy)²=0.25
cos²x+cos²y -2cosxcosy=0.25 ②
①+②得：
2-2cos(x-y)=0.5
cos(x-y)=3/4
所以,sin(x-y)=±√7/4
所以,原式=±√7/3
=[(sinxcosy-cosxsinx)/(cosxcosy) / [(cosxcosy+sinxsiny)/(cosxcosy)]
=(sinxcosy-cosxsinx)/(cosxcosy+sinxsiny)
=sin(x-y)/cos(x-y)
(sinx+siny)²=0.25
sin²x+sin²y+2sinxsiny =0.25 ①
(cosx-cosy)²=0.25
cos²x+cos²y -2cosxcosy=0.25 ②
①+②得：
2-2cos(x-y)=0.5
cos(x-y)=3/4
所以,sin(x-y)=±√7/4
所以,原式=±√7/3
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