cosX+cosY=1/2,sinX+sinY =1/4
则(cosX+cosY)^2=1/4,(sinX+sinY)^2=1/16
两式相加,得
2+2cosXcosY+2sinXsinY=1/4+1/16
则cosXcosY+sinXsinY=-27/32
因为cos(X-Y)=cosXcosY+sinXsinY
所以cos(X-Y)=-27/32
cosX+cosY=1/2,sinX+sinY =1/4
则(cosX+cosY)^2=1/4,(sinX+sinY)^2=1/16
两式相加,得
2+2cosXcosY+2sinXsinY=1/4+1/16
则cosXcosY+sinXsinY=-27/32
因为cos(X-Y)=cosXcosY+sinXsinY
所以cos(X-Y)=-27/32