On polynomials with simple trigonometric formulas

We show that the sequences of polynomials with zeros cot(mπ/(n+2)) and tan(mπ/(n+2)) are not orthogonal sequences with respect to any integral inner product. We give an algebraic formula for these polynomials, that is simpler than the formula originally derived by Cvijovic and Klinowski (1998). New sequences of polynomials with algebraic numbers as roots and closed trigonometric formulas are also derived by these methods