A new type of sensitive electro‐optic effect in a nematic liquid‐crystal (4‐cyano‐4’‐5‐alkyl‐bipheneyl) cell with polymer thin films is reported. Optical switching in a transmitted intensity of light passing through a cell is experimentally observed by dual low‐frequency modulation method using a triangular wave application. Dielectric relaxation effects in the thin polymer layer as part of the cell serve to reduce the effective voltage acting on the liquid‐crystal layer for lower frequencies but not for higher frequencies. The mean effective applied voltage to a liquid‐crystal layer is efficiently controlled by changing only the frequency.