  The article is devoted to establishing the distortion of the modulus of
families of paths in wide classes of mappings that admit branch points. In
particular, for mappings that are differentiable almost everywhere and have
$N$- and $N^{\,- 1}$-Luzin properties and are absolutely continuous on almost
all paths, we obtained the inverse Poletsky inequality with the so-called
cotangent dilatation. We have proved that, for inverse mappings, this
dilatation coincides with the so-called tangential dilatation of the
corresponding inverse mapping. In addition, we have proved that cotangent
dilatation is less than the outher or inner dilatation, in particular, may be
less than one on the set of positive Lebesgue measure
