若sinx-siny=-1/3,cosx-cosy=1/2,则cos(x-y)=?
人气:486 ℃ 时间:2019-08-26 06:11:08
解答
cosx-cosy=1/2 ,sinx-siny=-1/3
分别两边平方
(cosx)^2-2cosxcosy+(cosy)^2=1/4
(sinx)^2-2sinxsiny+(siny)^2=1/9
相加
且(cosx)^2+(sinx)^2=1 (cosy)^2+(siny)^2=1
2-2(cosxcosy+sinxsiny)=1/4+1/9=13/36
cos(x-y)=cosxcosy+sinxsiny
=(2-13/36)/2
=59/72
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