x^2-5x+6=0
x=2或3
不妨设tana=2,tanb=3
所以cosa=根号5/5,sina=2根号5/5
cosb=根号10/10,sinb=3根号10/10
tan(a+b)=(tana+tanb)/(1-tanatanb)=5/(-5)=-1
得a+b=135
cos(a-b)=cosacosb+sinasinb=7根号2/10