若sinα=根号10/10,β=arc cos(-根号5/5),0＜α＜π/2,求证:α+β=3π/4

sinα=根号10/10,0＜α＜π/2,则cosα=3根号10/10
β=arc cos(-根号5/5),故β>π/2,sinβ=(-2根号5/5),cosβ=(-根号5/5),
由于sin(α+β)=sinαcosβ+sinβcosα=(根号2)/2,且0＜α＜π/2,β>π/2则
α+β=3π/4