sin(x)+sin(y)=1 ・・・ ①
cos(x)+cos(y)=2/3 ・・・ ②
●①²+②²を考えると
1+2cos(x)・cos(y)+2sin(x)・sin(y)+1=1+(4/9)
整理して
2{cos(x)・cos(y)+sin(x)・sin(y)}=-5/9
両辺を2でわり
cos(x)・cos(y)+sin(x)・sin(y)=-5/18
加法定理:cos(x-y)=cos(x)・cos(y)+sin(x)・sin(y)より
cos(x-y)=-5/18