用sinα表示sin3α 用cosβ表示cos3β

sin3a=sin(2a+a)=sin2acosa+cos2asina
=2sinacos^2a+cos^2asina-sin^3a
=3sinacos^2a-sin^3a
=3sina(1-sin^2a)-sin^3a
=3sina-4sin^3a
cos3a=cos(2b+b)
=cos2bcosb-sin2bsinb
=cos^3b-cosbsin^2b-2sin^2bcosb
=cos^3b-3cosbsin^2b
=cos^3b-3cosb(1-cos^2b)
=4cos^3b-3cos

sin3a=sin(a+2a)=sinacos2a+cosasin2a=sina(1-2sin^2a)+2sina(1-sin^2a)
=sina(1-2sin^2a+2-2sin^2a)=sina(3-4sin^2a)
cos3β=cos(β+2β)=cosβcos2β-sinβsin2β=cosβ(2cos^2β-1)-2cosβ(1-cos^2β)
=cosβ(2cos^2β-1-2+2cos^2β)=cosβ(4cos^2β-3)