已知sinβ/sinα=cos(α+β),α、β为锐角.求证:tanβ=sin2α/(3-cos2α)

sinβ/sinα=cos(α+β),sinβ=sinα*cos(α+β),sinβ=sinα*(cosαcosβ-sinαsinβ),两边同时除以cosβtanβ=sinα*cosα-sin^2αtanβ,tanβ(1+sin^2α)=1/2sin2αtanβ(2+2sin^2α)=sin2αtanβ(2+2sin^2α-1+1...