  We study a single-particle density of states (DOS) in a model of
Tomonaga-Luttinger liquid with small (large) values of the Luttinger parameter
$K_\rc < 0.17$, ($K_\rc > 5.82$), in the charge sector. We explain that such
values of $K_\rc$ may be achieved by electron-phonon interactions without
generating the spin gap. We suggest that electron-phonon interactions can be
partially incorporated into the Tomonaga-Luttinger liquid scheme by introducing
frequency dependent $K_\rc(\omega)$. We demonstrate that when the low-frequency
asymptotic value $K_\rc(0) < 0.17$ or $K_\rc(0) > 5.82$, the single-particle
DOS has a pseudogap behavior in frequency where $\rho(\omega)/\omega$ vanishes
at small frequencies.
  The DOS exhibits a peak the position of which scales as $[K(0) +
K^{-1}(0)]\omega_0/2$ where $\omega_0$ is the characteristic phonon frequency.
