Using the matching polynomials of some particular graphs, the present work aims to establish several novel identities for Chebyshev polynomials of the first and second kind. Mainly, we give closed formulas for \(T_{r_{1}+r_{2}+\cdots + r_{s}}(x)\) and \(U_{r_{1}+r_{2}+\cdots + r_{s}}(x)\) , for any positive integers \(r_{i}\ge 2\) \((1\le i\le s)\) , where \(T_{n}(x)\) and \(U_{n}(x)\) are the \(n^{th}\) Chebyshev terms of the first and second kind, respectively. As an immediate application, several trigonometric identities are derived. Additionally, due to their connections with the classical Fibonacci and Lucas numbers, we derive several new identities for these latter sequences.
