# De Moivre's Theorem for Trig Identities

De Moivre's Theorem for Trig Identities

De Moivre's theorem, along with the binomial theorem, can be used to expand functions like or , where is an integer, into a sum of powers of trig functions consisting of a mixture of sines and cosines. In some cases it is possible to rewrite the expansion such that it contains all sines or all cosines by making use of the identity (x)+(x)=1.

cos(nx)

sin(nx)

n

2

sin

2

cos