We investigate the cosmological implications of studying galaxy clustering using a tomographic approach applied to the final BOSS DR12 galaxy sample , including both auto- and cross-correlation functions between redshift shells . We model the signal of the full shape of the angular correlation function , \omega ( \theta ) , in redshift bins using state-of-the-art modelling of non-linearities , bias and redshift-space distortions . We present results on the redshift evolution of the linear bias of BOSS galaxies , which can not be obtained with traditional methods for galaxy-clustering analysis . We also obtain constraints on cosmological parameters , combining this tomographic analysis with measurements of the cosmic microwave background ( CMB ) and type Ia supernova ( SNIa ) . We explore a number of cosmological models , including the standard \Lambda CDM model and its most interesting extensions , such as deviations from w _ { DE } = -1 , non-minimal neutrino masses , spatial curvature and deviations from general relativity using the growth-index \gamma parametrisation . These results are , in general , comparable to the most precise present-day constraints on cosmological parameters , and show very good agreement with the standard model . In particular , combining CMB , \omega ( \theta ) and SNIa , we find a value of w _ { DE } consistent with -1 to a precision better than 5 \% when it is assumed to be constant in time , and better than 6 \% when we also allow for a spatially-curved Universe .