The present paper aims to investigate the coupled nonlinear Schrodinger equation (NLSE) in magneto-optic waveguides having anti-cubic (AC) law nonlinearity. The solitons secured to magneto-optic waveguides with AC law nonlinearity are extremely useful to fiber-optic transmission technology. Three constructive techniques, namely, the (G'/G)-expansion method, the modified simple equation method (MSEM), and the extended tanh-function method are utilized to find the exact soliton solutions of this model. Consequently, dark, singular and combined dark-singular soliton solutions are obtained. The behaviours of soliton solutions are presented by 3D and 2D plots.