sinα=√5/5,
cosα=2√5/5,
tanβ=3
sinβ=3√10/10,
cosβ=√10/10,
cos(α-β)
=cosαcosβ+sinαsinβ
=2√5/5*√10/10+√5/5*3√10/10
=2√2/10+3√2/10
=√2/2
α-β=±45°