Using a $3.19~mathrm{fb}^{-1}$ data sample collected at an $e^+e^-$ center-of-mass energy of $E_{rm cm}=4.178$ GeV with the BESIII detector, we measure the branching fraction of the leptonic decay $D_s^+tomu^+ u_mu$ to be $mathcal{B}_{D_s^+tomu^+ u_mu}=(5.49pm0.16_{rm stat.}pm0.15_{rm syst.})times10^{-3}$. Combining our branching fraction with the masses of the $D_s^+$ and $mu^+$ and the lifetime of the $D_s^+$, we determine $f_{D_s^+}|V_{cs}|=246.2pm3.6_{rm stat.}pm3.5_{rm syst.}~mathrm{MeV}$. Using the $cto s$ quark mixing matrix element $|V_{cs}|$ determined from a global standard model fit, we evaluate the $D_s^+$ decay constant $f_{D_s^+}=252.9pm3.7_{rm stat.}pm3.6_{rm syst.}$,MeV. Alternatively, using the value of $f_{D_s^+}$ calculated by lattice quantum chromodynamics, we find $|V_{cs}| = 0.985pm0.014_{rm stat.}pm0.014_{rm syst.}$. These values of $mathcal{B}_{D_s^+tomu^+ u_mu}$, $f_{D_s^+}|V_{cs}|$, $f_{D_s^+}$ and $|V_{cs}|$ are each the most precise results to date.
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