(1)∵OP^2=(cosα-cosβ)^2+(sinα-sinβ)^2=(2√5/5)^2
∴ cosαcosβ+sinαsinβ=3/5
即 cos(α-β)=3/5
(2) 0＜α＜π/2,-π/2＜β＜0,∴0＜α-β＜π,sin(α-β)=4/5
-π/2＜β＜0,sinβ=-5/13 ∴ cosβ=12/13
Sinα=sin[β+(α-β)]=sinβcos(α-β)+cosβsin(α-β)
=-5/13*3/5+12/13*4/5
=33/65