  The detection of a voltage transverse to both an applied current and a
magnetic field is one of the most common characterization techniques in
solid-state physics. The corresponding component of the resistivity tensor
$\rho_{ij}$ can be separated into odd and even parts with respect to the
applied magnetic field. The former contains information, for example, about the
ordinary or anomalous Hall effect. The latter is typically ascribed to
experimental artefacts and ignored. We here show that upon suppressing these
artefacts in carefully controlled experiments, useful information remains. We
first investigate the well-explored ferromagnet CoFeB, where the even part of
$\rho_{yx}$ contains a contribution from the anisotropic magnetoresistance,
which we confirm by Stoner-Wohlfarth modelling. We then apply our approach to
magnetotransport measurements in $\rm Mn_5Si_3$ thin films with a complex
compensated magnetic order. In this material, the even part of the transverse
signal is sizable only in the low-spin-symmetry phase below $\approx 80$ K and
thus offers a simple and readily available probe of the magnetic order.
