sinx+siny=根号2 (1)
cosx+cosy=2根号3/3 (2)
(1)平方+(2)平方
2+2sinxsiny+2cosxcosy=2+4/3
cosxcosy+sinxsiny=2/3 (3)
cos (x-y)=2/3 (4)
(2)平方-(1)平方
cos2x+cos2y+2(cosxcosy-sinxsiny)=-2/3
2cos(x+y)cos(x-y)+2cos(x+y)=-2/3
把(4)代入,得到cos(x+y)=-1/5
所以cosxcosy-sinxsiny=-1/5 (5)
由(3)和(5)解得cosxcosy=7/30,sinxsiny=13/30
所以tanxtany=sinxsiny/cosxcosy=13/7