设α,β为锐角,且a=(sinα,-cos) b=(-cosβ,sinβ)a+b=(根号6/6,根号2/2)求cos(α+β) 求详解

问题描述:

设α,β为锐角,且a=(sinα,-cos) b=(-cosβ,sinβ)a+b=(根号6/6,根号2/2)求cos(α+β) 求详解

a+b=(sinα,-cosα) +(-cosβ,sinβ)=(sinα-cosβ,sinβ-cosα)=(√6/6,√2/2)sinα-cosβ=√6/6sinβ-cosα=√2/2分别平方,再相加:2-2(sinαcosβ+sinβcosα)=2/3sinαcosβ+sinβcosα=sin(α+β)=2/3co...