A detailed study of the exciton Zeeman spectra in diluted magnetic semicond
uctor Cd1-xCoxTe (x<0.5%) is carried out at T=1.6K from magnetoreflection a
nd magnetoabsorption in Faraday geometry. Analysis of <sigma>(+/-) reflecta
nce spectra within the polariton model determines the transverse eigenenerg
ies at different magnetic fields. The obtained energy pattern of the four Z
eeman components shows unusual features which we explain by taking into acc
ount the longitudinal-transverse splitting and the electron-hole exchange i
nteraction. Quantitative analysis of the energy spectrum carried out for va
rious cobalt compositions yields the determination of the exchange constant
N(0)beta= - 2.2+/-0.1.5 eV. We also estimate the zero-field energy separat
ion between \1,M > and \2,M > exciton states and the quadratic Zeeman shift
.