Tigonometric functions conversion from Mathematica back to Sage

Steps To Reproduce

Among all trigonometric functions, only $\sin$ and $\cos$ (and surprisingly all inverse functions) are correctly converted to their Sage equivalents from Mathematica when using sage() method on a mathematica object. Particularly Tan[x], Cot[x], Csc[x] and Sec[x] are converted to Tan(x), Cot(x), Csc(x) and Sec(x), i.e. the first letter is still uppercase and such functions are not recognized by Sage.

Expected Behavior

All trigonometric functions from Mathematica should be converted back to their Sage equivalents.

Actual Behavior

Capitalization of Tan, Cot, Sec and Csc from Mathematica prevails after conversion to Sage. The conversion table returns:

sage: sage.symbolic.expression.symbol_table['mathematica']
{('I', 0): I,
 ('True', 0): True,
 ('False', 0): False,
 ('Pi', 0): pi,
 ('E', 0): e,
 ('(1+Sqrt[5])/2', 0): golden_ratio,
 ('Log[2]', 0): log2,
 ('EulerGamma', 0): euler_gamma,
 ('Catalan', 0): catalan,
 ('Khinchin', 0): khinchin,
 ('Glaisher', 0): glaisher,
 ('Sin', 1): sin,
 ('Cos', 1): cos,
 ('ArcSin', 1): arcsin,
 ('ArcCos', 1): arccos,
 ('ArcTan', 1): arctan,
 ('ArcCot', 1): arccot,
 ('ArcCsc', 1): arccsc,
 ('ArcSec', 1): arcsec,
 ('Abs', 1): abs,
 ('Sqrt', 2): <function sqrt at 0x779e067cb9c0>,
 ('Surd', 2): real_nth_root,
 ('Arg', 1): arg,
 ('Re', 1): real_part,
 ('Im', 1): imag_part,
 ('Conjugate', 1): conjugate,
 ('Factorial', 1): factorial,
 ('Binomial', 2): binomial,
 ('ArcSinh', 1): arcsinh,
 ('ArcCosh', 1): arccosh,
 ('ArcTanh', 1): arctanh,
 ('ArcCoth', 1): arccoth,
 ('ArcSech', 1): arcsech,
 ('ArcCsch', 1): arccsch,
 ('Log', 1): log,
 ('PolyLog', 2): polylog,
 ('ProductLog', 2): lambert_w,
 ('HarmonicNumber', 1): harmonic_number,
 ('Zeta', 1): zeta,
 ('StieltjesGamma', 1): stieltjes,
 ('HurwitzZeta', 2): hurwitz_zeta,
 ('Gamma', 1): gamma,
 ('LogGamma', 1): log_gamma,
 ('Gamma', 2): gamma,
 ('Gamma', 3): <function _mathematica_gamma3 at 0x779db60b1120>,
 ('PolyGamma', 1): psi,
 ('PolyGamma', 2): psi,
 ('Beta', 2): beta,
 ('BesselJ', 2): bessel_J,
 ('BesselY', 2): bessel_Y,
 ('BesselI', 2): bessel_I,
 ('BesselK', 2): bessel_K,
 ('StruveH', 2): struve_H,
 ('StruveL', 2): struve_L,
 ('HankelH1', 2): hankel1,
 ('HankelH2', 2): hankel2,
 ('SphericalBesselJ', 2): spherical_bessel_J,
 ('SphericalBesselY', 2): spherical_bessel_Y,
 ('SphericalHankelH1', 2): spherical_hankel1,
 ('SphericalHankelH2', 2): spherical_hankel2,
 ('SphericalHarmonicY', 4): spherical_harmonic,
 ('EllipticE', 2): elliptic_e,
 ('EllipticE', 1): elliptic_ec,
 ('EllipticF', 2): elliptic_f,
 ('EllipticK', 1): elliptic_kc,
 ('EllipticPi', 3): elliptic_pi,
 ('JacobiND', 2): jacobi_nd,
 ('JacobiNS', 2): jacobi_ns,
 ('JacobiNC', 2): jacobi_nc,
 ('JacobiDN', 2): jacobi_dn,
 ('JacobiDS', 2): jacobi_ds,
 ('JacobiDC', 2): jacobi_dc,
 ('JacobiSN', 2): jacobi_sn,
 ('JacobiSD', 2): jacobi_sd,
 ('JacobiSC', 2): jacobi_sc,
 ('JacobiCN', 2): jacobi_cn,
 ('JacobiCD', 2): jacobi_cd,
 ('JacobiCS', 2): jacobi_cs,
 ('InverseJacobiND', 2): inverse_jacobi_nd,
 ('InverseJacobiNS', 2): inverse_jacobi_ns,
 ('InverseJacobiNC', 2): inverse_jacobi_nc,
 ('InverseJacobiDN', 2): inverse_jacobi_dn,
 ('InverseJacobiDS', 2): inverse_jacobi_ds,
 ('InverseJacobiDC', 2): inverse_jacobi_dc,
 ('InverseJacobiSN', 2): inverse_jacobi_sn,
 ('InverseJacobiSD', 2): inverse_jacobi_sd,
 ('InverseJacobiSC', 2): inverse_jacobi_sc,
 ('InverseJacobiCN', 2): inverse_jacobi_cn,
 ('InverseJacobiCD', 2): inverse_jacobi_cd,
 ('InverseJacobiCS', 2): inverse_jacobi_cs,
 ('JacobiAmplitude', 2): jacobi_am,
 ('ChebyshevT', 2): chebyshev_T,
 ('ChebyshevU', 2): chebyshev_U,
 ('LegendreP', 2): legendre_P,
 ('LegendreQ', 2): legendre_Q,
 ('LegendreP', 3): gen_legendre_P,
 ('LegendreQ', 3): gen_legendre_Q,
 ('HermiteH', 2): hermite,
 ('JacobiP', 4): jacobi_P,
 ('GegenbauerC', 3): gegenbauer,
 ('LaguerreL', 2): laguerre,
 ('LaguerreL', 3): gen_laguerre,
 ('PrimePi', 1): prime_pi,
 ('DiracDelta', 1): dirac_delta,
 ('HeavisideTheta', 1): heaviside,
 ('UnitStep', 1): unit_step,
 ('Sign', 1): sgn,
 ('KroneckerDelta', 2): kronecker_delta,
 ('AiryAi', 1): airy_ai,
 ('AiryAiPrime', 1): airy_ai_prime,
 ('AiryBi', 1): airy_bi,
 ('AiryBiPrime', 1): airy_bi_prime,
 ('FresnelS', 1): fresnel_sin,
 ('FresnelC', 1): fresnel_cos,
 ('HypergeometricPFQ', 3): hypergeometric,
 ('Hypergeometric1F1', 3): hypergeometric_M,
 ('HypergeometricU', 3): hypergeometric_U}

where tan, cot, sec and csc are missing.

Additional Information

Connected with issue #34087

Environment

OS: Ubuntu 24.04
Sage Version: 10.4
Python version: 3.12.3

Checklist

[X] I have searched the existing issues for a bug report that matches the one I want to file, without success.
[X] I have read the documentation and troubleshoot guide

sagemath / sage