tan3α=sin3α/s3α
=(sin2αsα+s2αsinα)/(s2αsα-sin2αsinα)
=(2sinαs^2(α)+s^2(α)sinα-sin^3(α))/(s^3(α)-sαsin^2(α)-2sin^2(α)sα)
上下同除以s^3(α)，得
tan3α=(3tanα-tan^3(α))/(1-3tan^2(α))
sin3α=sin(2α+α)=sin2αsα+s2αsinα
=2sinαs^2(α)+(1-2sin^2(α))sinα
=2sinα-2sin^3(α)+sinα-2sin^3(α)
=3sinα-4sin^3(α)
s3α=s(2α+α)=s2αsα-sin2αsinα
=(2s^2(α)-1)sα-2sαsin^2(α)
=2s^3(α)-sα+(2sα-2s^3(α))
=4s^3(α)-3sα
即
sin3α=3sinα-4sin^3(α)
s3α=4s^3(α)-3sα
