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Abstract In B c − $$ {B}_c^{-} $$ → J/ψ(→ μ + μ − )τ − ν ¯ τ $$ {\overline{\nu}}_{\tau } $$ decay, the three-momentum p τ − $$ {\boldsymbol{p}}_{\tau^{-}} $$ cannot be determined accurately due to the decay products of τ − inevitably include an undetected ν τ . As a consequence, the angular distribution of this decay cannot be measured. In this work, we construct a measurable angular distribution by considering the subsequent decay τ − → π − ν τ . The full cascade decay is B c − $$ {B}_c^{-} $$ → J/ψ(→ μ + μ − )τ − (→ π − ν τ ) ν ¯ τ $$ {\overline{\nu}}_{\tau } $$ , in which the three-momenta p μ + , p μ − $$ {\boldsymbol{p}}_{\mu^{+}},{\boldsymbol{p}}_{\mu^{-}} $$ , and p π − $$ {\boldsymbol{p}}_{\pi^{-}} $$ can be measured. The five-fold differential angular distribution containing all Lorentz structures of the new physics (NP) effective operators can be written in terms of twelve angular observables ℐ i (q 2 , E π ). Integrating over the energy of pion E π , we construct twelve normalized angular observables ℐ ̂ i $$ {\hat{\mathrm{\mathcal{I}}}}_i $$ (q 2) and two lepton-flavor-universality ratios R P L , T J / ψ $$ R\left({P}_{L,T}^{J/\psi}\right) $$ (q 2). Based on the B c → J/ψ form factors calculated by the latest lattice QCD and sum rule, we predict the q 2 distribution of all ℐ ̂ i $$ {\hat{\mathrm{\mathcal{I}}}}_i $$ and R P L , T J / ψ $$ R\left({P}_{L,T}^{J/\psi}\right) $$ both within the Standard Model and in eight NP benchmark points. We find that the benchmark BP2 (corresponding to the hypothesis of tensor operator) has the greatest effect on all ℐ i and R P L , T J / ψ $$ R\left({P}_{L,T}^{J/\psi}\right) $$ , except ℐ ̂ 5 $$ {\hat{\mathrm{\mathcal{I}}}}_5 $$ . The ratios R P L , T J / ψ $$ R\left({P}_{L,T}^{J/\psi}\right) $$ are more sensitive to the NP with pseudo-scalar operators than the ℐ i . Finally, we discuss the symmetries in the angular observables and present a model-independent method to determine the existence of tensor operators.