Question

已知sin(α+β)=2/3 sin(α-β)=1/5 求tanα/tanβ=?

Answer 1

sin(α+β)=2/3
sinαcosβ+cosαsinβ=2/3 ①
sinαcosβ-cosαsinβ=1/5 ②
①+②
2sinαcosβ=13/15
①-②
2cosαsinβ=7/15
tanα/tanβ=13/7

Answer 2

sin(α+β)=2/3 =sinαcosβ+cosαsinβ=2/3
sin(α-β)=sinαcosβ-cosαsinβ=1/5
2sinαcosβ=13/15
cosαsinβ=7/15
tanα/tanβ=sinαcosβ/cosαsinβ()13/15)/(7/15)=13/7