已知sinx+siny=1/2,cosx+cosy=1/3,求cos²((x-y)/2)
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已知sinx+siny=1/2,cosx+cosy=1/3,求cos²((x-y)/2)
(sinx+siny)^2=1/4 ①
(cosx+cosy)^2=1/9 ②
①+ ②:2cosxcosy+(cos x) ²+(cos y) ²+2sinxsiny+(sinx) ²+(siny) ²=13/36
2cosxcosy+2sinxsiny+2=13/36
cosxcosy+sinxsiny=-59/72
即cos(x-y)=-59/72
而cos²((x-y)/2)=[1+cos(x-y)]/2=13/144
(cosx+cosy)^2=1/9 ②
①+ ②:2cosxcosy+(cos x) ²+(cos y) ²+2sinxsiny+(sinx) ²+(siny) ²=13/36
2cosxcosy+2sinxsiny+2=13/36
cosxcosy+sinxsiny=-59/72
即cos(x-y)=-59/72
而cos²((x-y)/2)=[1+cos(x-y)]/2=13/144
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