tan(x+y)=7,tanx*tany=2/3,则cos(x-y)=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/29 03:07:05
![tan(x+y)=7,tanx*tany=2/3,则cos(x-y)=?](/uploads/image/z/6915142-46-2.jpg?t=tan%28x%2By%29%3D7%2Ctanx%2Atany%3D2%2F3%2C%E5%88%99cos%EF%BC%88x-y%EF%BC%89%3D%3F)
tan(x+y)=7,tanx*tany=2/3,则cos(x-y)=?
tan(x+y)=7,tanx*tany=2/3,则cos(x-y)=?
tan(x+y)=7,tanx*tany=2/3,则cos(x-y)=?
由题易得
tanx+tany=7/3
tanx*tany=2/3
所以
tanx=1/3
tany=2
sin x =1/根号10
sin y =2/根号5
原式=3/2*2/3*cos x *cos y +sin x *sin y
=3/2*tan x *tan y *cos x *cos y +sin x *sin y
=5/2*sin x *sin y
=根号2/2