  1T$^\prime$-MoS$_2$ exhibits valley-spin-polarized tilted Dirac bands in the
presence of external vertical electric field and undergoes a topological phase
transition between the topological insulator and band insulator around the
critical value of the electric field. Within the linear response theory, we
theoretically investigate the anisotropic longitudinal optical conductivities
of tilted Dirac bands in both undoped and doped 1T$^\prime$-MoS$_2$, including
the effects of the vertical electric field. The influence of the spin-orbit
coupling gap, band tilting, and vertical electric field on the optical
conductivities of tilted Dirac bands is revealed. A theoretical scheme for
probing the topological phase transition in 1T$^\prime$-MoS$_2$ via exotic
behaviors of longitudinal optical conductivities is proposed. The results for
1T$^\prime$-MoS$_2$ are expected to be qualitatively valid for other monolayer
tilted gapped Dirac materials, such as $\alpha$-SnS$_2$, TaCoTe$_2$, and
TaIrTe$_4$, due to the similarity in their band structures.
