Nuclear medium effects in the deep inelastic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mmultiscripts><…

The nuclear medium effects are studied in the $\nu_\tau/\bar\nu_\tau$ interactions from nuclei deep inelastic scattering (DIS) region and applied to $^{40}Ar$ nucleus obtain cross sections energy of proposed DUNE experiment. free nucleon structure functions ($F_{iN}(x,Q^2);~(i=1-5)$) have been calculated at next-to-leading order (NLO) using Martin-Motylinski-Harland Lang-Thorne 2014 as well Coordinated Theoretical-Experimental Project on QCD parameterizations for parton distribution (PDFs) including effect perturbative nonperturbative corrections \cite{Ansari:2020xne}. These then convoluted with spectral function ($F_{iA}(x,Q^2);~(i=1-5)$). takes into account Fermi motion binding nucleons correlations within nucleus. used calculate sections. Moreover, contribution $\pi$ $\rho$ mesons due shadowing antishadowing relevant kinematic Bjorken variable $x$ also included. numerical results presented compared obtained phenomenological approach nCTEQnu.