ab不共线的两个向量,a=(cosα,sinα),b=(cosβ,sinβ),若α属于(-π/4,π/4),β=π/4,且ab=3/5,求sinα

ab=3/5=cosαcosβ+sinαsinβ=cos(α-β)α属于(-π/4,π/4),β=π/4,α-β∈(-π/2,0)所以sin(α-β)=-4/5sinα=sin[(α-β)+β]=sin(α-β)cosβ+cos(α-β)sinβ=-4/5×根号2/2+3/5×根号2/2=-根号2/10...