Bound states for generalized trigonometric and hyperbolic Pöschl–Teller potentials

We use the "tridiagonal representation approach" to solve time-independent Schr\"odinger equation for bound states of generalized versions trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials do not belong conventional class exactly problems. The solutions are finite series square integrable functions written in terms Jacobi polynomial.