In Ramanujan's Lost Notebooks and the famous Slater's list, there are numerous identities of Rogers–Ramanujan type. It is known that $q$-orthogonal polynomials are closely related to these identities. Recently, G.E. Andrews found a surprising phenomenon that the classical orthogonal polynomials also could enter naturally into the world of $q$. More precisely, by using Bailey’s lemma, Andrews applied Chebyshev polynomials of the third and the fourth kinds to study Dyson's “favorite” identity of Rogers–Ramanujan type. In this talk, we will extend Andrews' way to find further applications of Chebyshev polynomials of the third kind in the study of Rogers–Ramanujan type identities. As consequences, we obtain a companion identity to Dyson's favorite identity. We also derive a number of identities related to false theta functions, Appell-Lerch series and Hecke–type double series involving indefinite quadratic forms.