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