  Considering $Z(3930)$ and $X(4160)$ as $\chi_{c2}(2P)$ and $\chi_{c2}(3P)$
states, the semileptonic and nonleptonic of $B_c$ decays to $Z(3930)$ and
$X(4160)$ are studied by the improved Bethe-Salpeter(B-S) Method. The form
factors of decay are calculated through the overlap integrals of the meson wave
functions in the whole accessible kinematical range. The influence of
relativistic corrections are considered in the exclusive decays. Branching
ratios of $B_c$ weak decays to $Z(3930)$ and $X(4160)$ are predicted. Some of
the branching ratios are: $Br(B_c^+\to
Z(3930)e^+\nu_e)$$=(3.03^{+0.09}_{-0.16})\times 10^{-4}$ and $Br(B_c^+\to
X(4160)e^+\nu_e)$$=(3.55^{+0.83}_{-0.35})\times 10^{-6}$. These results may
provide useful information to discover $Z(3930)$ and $X(4160)$ and the
necessary information for the phenomenological study of $B_c$ physics.
