Chebyshev polynomials have been studied or used from several perspectives, including in numerical analysis and algebra. For instance, this writer studied the Chebyshev polynomials of the first kind from the perspective of the Galois Group of equations. It was shown that the Galois Group of the Chebyshev polynomials of the first kind of prime degree is isomorphic to the cyclic group of order 2. Relevant theorems and proofs were provided in the paper. Please see:
*Oluwade, Bamidele (‘Dele) (2010), ‘The Galois Group of the Chebyshev Polynomials of the First
Kind of Prime Degree’, African Journal of Computing & ICT, Vol. 3, Nos 1 & 2, pp. 21 – 27; https://afrjcict.net