令γ=α+β则 3sin(γ-α)=sin(γ+α)得 3sinγcosα-3cosγsinα=sinγcosα+cosγsinα即 2sinγcosα=4cosγsinα =>sinγ/cosγ=4sinα/2cosα tanγ=2tanα 即 得证tan(α+β)=2tanα
