1. The problem statement, all variables and given/known data The nth order Chebyshev polynomial is defined by Tn(x)= cos( n arccos(x) ) , n is a positive integer; -1<= x <= 1. Using the de Moivre theorem, show that Tn(x) has the polynomial representation Tn(x)= 1/2 [(x+sqrt(x2-1))n+(x-sqrt(x2-1))n] 3. The attempt at a solution I really have no idea where to begin. Only thing i can come up is to try to simplify cos (n arccos(x)) , but i get stuck.