令cosa+cosb=t
则有t^2+(√2/2)^2=2+2(cosacosb+sinasinb)=2+2cos(a-b)
t^2=3/2+2cos(a-b)
-1≤cos(a-b)≤1
即-1/2≤t^2≤7/2
-√14/2≤t≤√14/2