若α，β为锐角，且满足cosα=4/5，cos（α+β）=3/5，则sinβ的值是

A.3/5 B.1/5 C.17/25 D.7/25

cosα=4/5，得sinα=3/5；cos(α+β)=3/5，得sin(α+β)=4/5

2cosαcos(α+β)=2??4/5??3/5
cos[α+(α+β)]+cosβ=24/25
cosαcos(α+β)-sinαsin(α+β)+cosβ=24/25
4/5??3/5-3/5??4/5+cosβ=24/25
cosβ=24/25

得sinβ=7/25

解 ∵a是锐角 即a∈(0.π/2) ∴a+π/4∈(π/4,3π/4) ∴sin(a+π/4)>0 ∵cos(a+π/4)=3/5——利用sin²a+cos²a=1 ∴sin(a+π/4)=4/5 ∴sina =sin[(a+π/4)-π/4] =sin(a+π/4)cosπ/4-cos(a+π/4)sinπ/4 =√2/2(4/5-3/5) =√2/10