sin3a =sin(2a+a)=sin2acosa+cos2asina=2sina(1-sin²a)+(1-2sin²a)sina=3sina-4sin³a
cos3a=cos(2a+a)=cos2acosa-sin2asina=(2cos²a-1)cosa-2(1-cos²a)cosa=4cos³a-3cosa
tan3α＝sin3α/cos3α
＝(sin2αcosα＋cos2αsinα)/(cos2αcosα-sin2αsinα)
＝(2sinαcos^2(α)＋cos^2(α)sinα－sin^3(α))/(cos^3(α)－cosαsin^2(α)－2sin^2(α)cosα)
上下同除以cos^3(α),得：
tan3α＝(3tanα－tan^3(α))/(1-3tan^2(α))