In this short note we prove that two trigonometric quadrature formulae which are very often in applications, are equivalent to the trigonometric version of the Gauss-Radau formulas with respect to the Chebyshev weight of the first kind on $(-1,1)$. Also, we give a short account on the classical results of Gauss-Radau quadrature rules which are related to the Chebyshev weight functions.