  The trigonometric double affine Hecke algebra $\mathbf{H}_c$ for an
irreducible root system depends on a family of complex parameters $c$ Given two
families of parameters $c$ and $c'$ which differ by integers, we construct the
translation functor from $\mathbf{H}_{c}\operatorname{-Mod}$ to
$\mathbf{H}_{c'}\operatorname{-Mod}$ and prove that it induces equivalence of
derived categories. This is a trigonometric counterpart of a theorem of Losev
on the derived equivalences for rational Cherednik algebras.
