如果cosx+cosy-cos(x+y)=1.5,x,y为锐角,求x和y.

题目

如果cosx+cosy-cos(x+y)=1.5,x,y为锐角,求x和y.

答案

cosx+cosy-cos(x+y)=3/2
--->2[cos(x+y)/2]^2-2[cos(x+y)/2][cos(x-y)/2]+1/2=0
[-2cos(x-y)/2]^2-4>=0
--->[cos(x-y)/2]^2>=1
[cos(x-y)/2]^2=1
x、y(0,兀) --->(x-y)/2(-兀/2,兀/2).
x=y,
x=y=兀/3.