0<α<π/2<β<π，
sinα=3/5
cosα=4/5
cosa(α+β)=-4/5
cosaαcosβ-sinαsinβ=-4/5
4/5*cosβ-3/5*sinβ=-4/5
4cosβ-3sinβ=-4
4cosβ=3sinβ-4
16(cosβ)^2=9(sinβ)^2-24sinβ+16
16-16(sinβ)^2=9(sinβ)^2-24sinβ+16
-16(sinβ)^2=9(sinβ)^2-24sinβ
25(sinβ)^2-24sinβ=0
(25sinβ-24)sinβ=0
sinβ=24/25或sinβ=0（舍去，π/2<β<π)
所以sinβ=24/25