  The polarization effects in the one-meson radiative decay of the polarized
$\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, have been investigated. We
present the analytical results for the $t-$distribution of the partial
differential widths, which responsible for different polarization phenomena, in
the case of the photon energy cut: $\omega>X$. These quantities depend on the
invariant mass squared $t$ of the pseudoscalar meson and photon and the photon
energy cut $X.$ Our analytical formulae, in terms of the weak vector and
axial-vector form factors, describing the structure-dependent part of the decay
amplitude, are valid also for the decay $\tau^{\pm}\to
K^{\pm}\,\nu_\tau\,\gamma$ after trivial substitutions of the corresponding
constants. We demonstrate the essential decrease of the inner bremsstrahlung
contribution in comparison with the structural one with increase of the photon
cut energy. In numerical calculations the vector and axial-vector form factors
are determined using the chiral effective theory with resonances (R$\chi$T).
