Question

已知sinβ=msin(2α+β),切tan(α+β)\tanα=3,则实数m的值为

Answer 1

sin[(α+β)-α]=msin[(α+β)+α]

sin(α+β)cosα-cos(α+β)sinα=msin(α+β)cosα+mcos(α+β)sinα

(1-m)sin(α+β)cosα=(1+m)cos(α+β)sinα

tan(α+β)=[(1+m)/(1-m)]tanα

所以(1+m)/(1-m)=3

m=0.5