sinα=sin[(α＋β)-β]=sin(α＋β)cosβ－cos(α＋β)sinβ＝3/5
而α∈(π/2,π),所以tanα=-3/4
所以tan(π/4－α)=(tanπ/4-tanα)/(1+tanπ/4*tanα)
=(1+3/4)/(1-3/4)
=7