Question

sinx+siny=根号3 cosx+cosy=2根号3/3 求tanxtany

错了，第一个我等于根号2

Answer 1

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

Answer 2

解:
两条件式平方相加,得
2+2cos(x-y)=13/3
→cos(x-y)=7/6矛盾了题目有问题sinx+siny=根号3要改为根号2 解:
两条件式平方相加,得
2+2cos(x-y)=10/3
→cos(x-y)=2/3 …… (1)
两条件式平方相减,得
cos2x+cos2y+2cos(x+y)=-2/3
→2cos(x+y)cos(x-y)+2cos(x+y)=-2/3
代(1)代入,得
4/3*cos(x+y)+2cos(x+y)=-2/3
→cos(x+y)=-1/5 …… (2)
(1)+(2),得2cosxcosy=7/15 …… (3)
(1)-(2),得2sinxsiny=13/15 …… (4)
(4)÷(3),得tanxtany=13/7.