sin(α+β)=sinαcosβ+cosαsinβ=2/3 ①
sin(α-β)=sinαcosβ-cosαsinβ=1/5 ②
联立①②:sinαcosβ=13/15;cosαsinβ=7/15
tanα/tanβ=tanα×1/tanβ
=sinα/cosα×cosβ/sinβ
=sinαcosβ/cosαsinβ
=(13/15)×(15/7)=13/7
sin(α+β)=2/3,sin(α-β)=1/5,
sinαcosβ+cosαsinβ=2/3 (1)
sinαcosβ-cosαsinβ=1/5 (2)
(1)+(2)
2sinαcosβ=2/3+1/5=13/15 (3)
(1)-(2)
2cosαsinβ=2/3-1/5=7/15 (4)
(3)/(4)
tanα/tanβ=13/7