α∈(π/2,π),
所以cosα<0
(sinα)^2+(cosα)^2=0
sinα=8/17
所以cosα=-15/17
β∈(π/2,π),
所以sinβ>0
(sinβ)^2+(cosβ)^2=0
cosβ=-5/13
所以sinβ=12/13
cos(α+β)=cosαcosβ-sinαsinβ
=(-15/17)*(-5/13)-(8/17)*(12/13)
=-21/221