已知sinx+siny=0.4,cosx+cosy=1.2,求cos(x-y)
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已知sinx+siny=0.4,cosx+cosy=1.2,求cos(x-y)已知sinx+siny=0.4,cosx+cosy=1.2,求cos(x-y)已知sinx+siny=0.4,cosx+c
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sinx+siny=0.4
(sinx+siny)^2=0.16
(sinx)^2+2sinxsiny+(siny)^2=0.16
cosx+cosy=1.2
(cosx+cosy)^2=1.44
(cosx)^2+2cosxcosy+(cosy)^2=1.44
两个式子相加:
2+2sinxsiny+2cosxcosy=1.6
2(sinxsiny+cosxcosy)=-0.4
2cos(x-y)=-0.4
cos(x-y)=-0.2
上两式分别平方并相加得
2+2(cosxcosy+sinxsiny)=1.6
cos(x-y)=cosxcosy+sinxsiny=-0.2
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