cos(a+β)=1/5==>cosαcosβ-sinαsinβ=1/5 ①
cos(a-β)=3/5==>,cosαcosβ+sinαsinβ=3/5 ②
①+②:2cosαcosβ=4/5 ,cosαcosβ=2/5
②-①:2sinαsinβ=2/5 sinαsinβ=1/5
∴tana·tanβ=sinα/cosα*sinβ/cosβ
=sinαsinβ/(cosαcosβ)=(1/5)/(2/5)=1/2