Odpowiedź :
a)
[tex][tex]sin3\alpha =sin(\alpha +2\alpha )=sin\alpha cos2\alpha +cos\alpha sin2\alpha =sin\alpha (cos^{2}\alpha -sin^{2} \alpha )+cos\alpha (2sin\alpha cos\alpha )=sin\alpha cos^{2}\alpha -sin^{3}\alpha +2sin\alpha cos^{2}\alpha =sin(1-sin^{2}\alpha )-sin^3\alpha +2sin\alpha 91+sin^2\alpha )=sin\alpha -sin^3\alpha +2sin\alpha -sin^3\alpha =3sin\alpha -4sin^3\alpha[/tex][/tex]
b)
[tex]cos3\alpha =cos(2\alpha+\alpha)=cos2\alphacos\alpha-sin2\alphasin\alpha=(2cos^{2} \alpha -1) cos\alpha - (2sin\alpha cos\alpha)sin\alpha=2cos^{3}\alpha -cos\alpha -2sin^{2} \alpha cos\alpha=cos\alpha(2cos^{2}\alpha-1-2sin^{2} \alpha)=cos\alpha(2(cos^{2} \alpha-1))=cos\alpha(4cos^{2} \alpha-2-1)=cos\alpha(4cos^{2} \alpha-3) = 4cos^{3}\alpha - 3cos\alpha[/tex]