Trigonometric identities, angular Schr\"{o}dinger equations and a new family of solvable models

Angular parts of certain solvable models are studied. We find that an extension of this class may be based on suitable trigonometric identities. The new exactly solvable Hamiltonians are shown to describe interesting two- and three-particle systems of the generalized Calogero, Wolfes and Winternitz-Smorodinsky types.