De Moivre's Theorem

[Guest]

De Moivre's Theorem states that if

z = r cos theta + i r sin theta then
z^n = r^n(cos n*theta + i sin n*theta) for all natural numbers...


How could I use this theorem to prove that
cos 5(theta) = 16 cos^5(theta) - 20 cos^5(theta) + 5 cos(theta)

thanks

 

[royhaas]

Let n=5, expand and equate the real parts.