
Pou�ijeme k tomuto vyj�d�en� Moivreovy a binomick� v�ty:\newline
Z Moivreovy v�ty: ${(\cos\alpha + i\sin\alpha)}^5=\cos5\alpha + i\sin5\alpha$
\newline
Z binomick� v�ty: ${(\cos\alpha + i\sin\alpha)}^5=\cos^5\alpha+5i\cos^4\alpha
\sin\alpha-\newline-10\cos^3\alpha\sin^2\alpha-10i\cos^2\alpha\sin^3\alpha+
5\cos\alpha\sin^4\alpha+i\sin^5\alpha$\newline
Porovn�n�m re�ln�ch a imagin�rn�ch ��st� obou ��sel dostaneme po�adovan� vztahy:
$$
   \cos5\alpha=\cos^5\alpha-10\cos^3\alpha\sin^2\alpha+5\cos\alpha\sin^4\alpha
$$
\centerline a
$$
   \sin5\alpha=\sin^5\alpha-10\sin^3\alpha\cos^2\alpha+5\sin\alpha\cos^4\alpha
$$
