  At present, the Boer-Mulders function for a given quark flavour has been
extracted from data on semi-inclusive deep inelastic scattering using the
simplifying, but theoretically inconsistent, assumption that it is proportional
to the Sivers function for each quark flavour. In this paper, using the latest
semi-inclusive deep inelastic COMPASS deuteron data on the
$\langle\cos\phi_h\rangle$ and $\langle\cos 2 \phi_h\rangle$ asymmetries we
extract the collinear $x_B$-dependence of the Boer-Mulders function for the sum
of the valence quarks $Q_V=u_V + d_V$ in an essentially model independent way,
and find a significant disagreement with the published results. Our analysis
also yields interesting information on the transverse momentum dependence of
the unpolarized quark distribution and fragmentation functions.
