已知sinα=(√5)/5,sinβ=(√10)/10,且α、β都是区间（0，π/6)的角，求证：α+β=π/4

sinα=√5/5
α为锐角 则cosα>0
(cosα)^2+(sinα)^2=1
cosα=2√5/5

sinβ=√10/10
α为锐角 则cosβ>0
(cosβ)^2+(sinβ)^2=1
cosβ=3√10/10

sin(α+β)=sinαcosβ+cosαsinβ
=√5/5*3√10/10+2√5/5*√10/10
=(5√50)/50
=5/√50
=5/(5√2)
=√2/2

α、β都是区间(0，π/6)的角
0<α+β<π/6*3=π/3
所以α+β= π/4