Let a = (COS α, sin β) and B = (COS β, sin α), then α - β =? 0

Let a = (COS α, sin β) and B = (COS β, sin α), then α - β =? 0

a.b=1/2
(cosα,sinβ).(cosβ,sinα)=1/2
cosαcosβ+sinαsinβ=1/2
cos(α-β)= 1/2
α-β =π/3