We provide a combinatorial proof of the trigonometric identity cos(nθ) = Tncos(θ),
where Tn is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind.
© 2010 Elsevier B.V.
Benjamin, A.T., Ericksen, L., Jayawant, P., & Shattuck, M. (2010). Combinatorial trigonometry with Chebyshev polynomials. Journal of Statistical Planning and Inference, 140(8): 2157-2160. DOI: 10.1016/j.jspi.2010.01.011.