a·b=2sina+5cos²a=22/5
得：cos²a=22/25-2sina/5
代入sin²a+cos²a=1
得：sin²a-2sina/5-3/25=0
25sin²a-10sina-3=0
(5sina+1)(5sina-3)=0
sina=-1/5或sina=3/5
因为a∈（π/2,π)
所以,sina>0
所以,sina=3/5
则：cosa=-4/5
tana=-3/4
tan(a+π/4)=(tana+1)/(1-tana)=1/7