cos(α+β)=1/3,cos(α-β)=1/4,求cosα-cosβ,
问题描述：
cos(α+β)=1/3,cos(α-β)=1/4,求cosα-cosβ,
答
cos(α+β)=1/3,cos(α-β)=1/4,求cosα-cosβcos(α+β)=cosαcosβ-sinαsinβ=1/3.(1)cos(α-β)=cosαcosβ+sinαsinβ=1/4.(2)(1)+(2)得2cosαcosβ=7/12,即cosαcosβ=7/24.(3)(2)-(1)得2sinαsinβ=-1/12,即s...