已知α,β为锐角,向量a=(cosα,sinα),b=(cosβ,sinβ),c=(1/2,-1/2)

(1)a·b=cosαcosβ+sinαsinβ
=cos（α-β）=√2/2
a·c=1/2cosα-1/2sinα
=√2/2cos（α+π/4）=(√3-1)/4
故cos（α+π/4）=(√6-√2)/4>0
故sin（α+π/4）=(√6+√2)/4
故sinα=sin（α+π/4-π/4)
=sin（α+π/4）cosπ/4-cos(α+π/4）sinπ/4
=1/2
因0