Neglecting the magnetic gradient drift effects, we derive a simplified version of the integraJ eigenvalue equations for perturbations of electrostatic potential, and the perpendicular and parallel components of magnetic vector potential in plasmas of sheared slab geometry. The electron temperature gradient (ETG) instability in high beta plasmas is studied with the equations and the corresponding computer code. The preliminary results indicate that the coupling to perturbation of the perpendicular component of the magnetic vector potential has strong destabilization effects on ETG instabilities in contrast to the stabilization effects from the coupling to that of the parallel component when the magnetic gradient drift is not taken into account.