Spin-polarized photoluminescence spectra in tilted fields were measured to 60 T at 1.5 K in a modulation-doped n-CdTe/(Cd,Mg,Mn)Te single quantum well with the thickness of 10 nm and the sheet electron density of 5.7×10 11 cm-2. A new σ--polarized emission peak emerged on the higher energy side of a main peak in the σ- polarization around the Landau filling factor ν of 1. Magnetic field dependence of the main peak energy exhibited a novel two-step like behavior around ν of 0.9 and that of the peak intensity was observed to take local maximum there. With increasing the field angle, these features of the main peak disappeared. Temperature dependence of the profiles of these emission peaks was also investigated to 40 T between 1.3 and 20 K. Relative intensity of the new emission peak to the main one was found to decrease with increasing temperature. Taking into consideration that a larger Zeeman gap should be unfavorable to a spin-singlet charged exciton (X -) and degradation of quantum limit by thermal excitation could be unfavorable to a spin-triplet X -, the new peak is assigned to the spin-triplet X - and the main peak to the spin-singlet X -.