Chebyshev Polynomials and the Minimal Polynomial of cos(2π/n)

The minimal polynomial of cos( 2 pi/ n) allows one to realize the value of cos( 2 pi/ n) as the root of a polynomial with rational coefficients. These polynomials prove to be instrumental in expressing some relations satisfied by Chebyshev polynomials as a product. In this article a few relations satisfied by Chebyshev polynomials of the first and second kind and the minimal polynomial of cos( 2 pi/ n) are presented. The proof of the main theorem shows how cyclotomic polynomials can be used to link these two kinds of polynomials.