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Convert exponential form to hyperbolic functions

Is there a method to convert expression containing exponentials like (e^a + e^-a) / 2 to hyperbolic functions? I tried to even call maxima functions directly, but thinks like cosh(a)._maxima_().exponentialize().demoivre() still don't give me cosh(a) back but instead return the form in exponentials.

Convert exponential form to hyperbolic functions

Is there a method to convert expression containing exponentials like (e^a + e^-a) / 2 to hyperbolic functions? I tried to even call maxima functions directly, but thinks like cosh(a)._maxima_().exponentialize().demoivre() still don't give me cosh(a) back but instead return the form in exponentials.