Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart

We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schrödinger problems defined by potentials V(x;?,?)=4?2cosh4(x)+V1(?,?)cosh2(x)+???1tanh2(x) and U(x;?,?)=?4?2cos4(x)?V1(?,?)cos2(x)+???1tan2(x), found anti-isospectral transformation of former. use three methods: a direct polynomial expansion, which shows relation between expansion order shape potential function; comparison to confluent Heun equation (CHE), has been shown provide only part spectrum in different quantum mechanics problems, Lie algebras, proven reveal hidden algebraic structures this kind spectral problems.