Relations between the K_(l3) and tau --> K pi nu_tau decays

We investigate the relations between the K_{l3} and tau --> K pi nu_tau decays using the meson dominance approach. First, the experimental branching fractions (BF) for K^-_{e3} and K^0_{e3} are used to fix two normalization constants (isospin invariance is not assumed). Then, the BF of tau^- --> K^*(892)^- nu_tau is calculated in agreement with experiment. We further argue that the nonzero value of the slope parameter lambda_0 of the K^-_{mu3} and K^0_{mu3} form factors f_0(t) implies the existence of the tau^- --> K_0^*(1430)^- nu_tau decay. We calculate its BF, together with BF's of the K^-_{mu3}, K^0_{mu3}, tau- --> K^- pi^0 nu_tau, and tau- --> antiK^0 pi^0 nu_tau decays, as a function of the lambda_0 parameter. At some value of lambda_0, different for charged and neutral kaons, calculated BF's seem to match existing data and a prediction is obtained for the tau^- --> K pi nu decays going through the K_0^*(1430)^- resonance.