  In this article, we take the point of view that the charmed mesons
$D_{s0}(2317)$ and $D_{s1}(2460)$ with the spin-parity $0^+$ and $1^+$
respectively are the conventional $c\bar{s}$ states, and calculate the strong
coupling constants $G_S$(for $<D_s^* \phi | D_{s0}>$) and $G_A$(for $<D_s \phi
| D_{s1}>$) in the framework of the light-cone QCD sum rules approach. The
strong coupling constants $G_S$ and $G_A$ are related to the basic parameter
$\hat{\mu}$ in the heavy quark effective Lagrangian, the numerical value is
larger than the existing estimation. With the assumption of the vector meson
dominance of the intermediate $\phi(1020)$, we study the radiative decays
$D_{s0}\to D_s^* \gamma $ and $D_{s1}\to D_s \gamma $.
