  We investigate the structure of the $D_{s1}(2460,2536) (J^P=1^+)$ mesons via
analyzing the semileptonic $B_{c}\to D_{s1}l^+l^-$, $l=\tau, \mu, e$ and
$B_{c}\to D_{s1}\nu\bar{\nu}$ transitions in the framework of the three--point
QCD sum rules. We consider the $D_{s1}$ meson in two ways, the pure
$|c\bar{s}>$ state and then as a mixture of two $|^3P_1>$ and $|^1P_1>$ states.
Such type rare transitions take place at loop level by electroweak penguin and
weak box diagrams in the standard model via the flavor changing neutral current
transition of $b \to s$. The relevant form factors are calculated taking into
account the gluon condensate contributions. These form factors are numerically
obtained for $|c\bar s>$ case and plotted in terms of the unknown mixing angle
$\theta_s$, when the $D_{s1}$ meson are considered as mixture of two $|^3P_1>$
and $|^1P_1>$ states. The obtained results for the form factors are used to
evaluate the decay rates and branching ratios. Any future experimental
measurement on these form factors as well as decay rates and branching
fractions and their comparison with the obtained results in the present work
can give considerable information about the structure of this meson and the
mixing angle $\theta_s$.
