  The electroweak symmetry breaking (EWSB) mechanism is still an undecided
question in particle physics. We propose to utilize the single top quark and
Higgs associated production ($th$), $Zh$ production via gluon fusion at the LHC
to probe the couplings between the Higgs and the gauge bosons and further to
test the EWSB. We demonstrate that the $th$ and $gg\to Zh$ productions are
sensitive to the relative sign of couplings ($ht\bar{t}$, $hWW$) and
($ht\bar{t}$, $hZZ$), respectively. We find that the relative sign between
$hWW$ and $hZZ$ couplings could be fully determined after combining the present
measurements from $gg\to h$, $t\bar{t}h$ and the $th$, $Zh$ channels at the 13
TeV LHC, and this conclusion is not sensitive to the possible new physics
contribution induced by $Zt\bar{t}$ couplings in the $gg\to Zh$ production.
