inconsistent treatment of hyperbolic functions with simplify

[terben]

Here is my Ipython interaction with SymPy:

In [1]: import sympy as sp

In [2]: x, y = sp.symbols('x, y', real=True)

In [3]: sp.simplify(sp.sinh(x)**2 + 1)
Out[3]: cosh(x)**2

In [4]: sp.simplify(sp.sinh(x + y)**2 + 1)
Out[4]: cosh(x + y)**2

In [5]: sp.simplify(sp.cosh(x)**2 - 1)
Out[5]: sinh(x)**2

In [6]: sp.simplify(sp.cosh(x + y)**2 - 1)
Out[6]: cosh(x + y)**2 - 1

The results of the first three In[]- expressions meet my expectations but I would expect the Output of the last expression to yield sp.sinh(x + y)**2.

In [7]: sp.__version__
Out[7]: '1.12'

[smichr]

Given that [4] works, it is curious that [6] does not.

[terben]

Given that [4] works, it is curious that [6] does not.

Yes! I am currently doing quite a lot of calculations involving hyperbolic functions and it is the third issue of this kind. Unfortunately, I do not know anything about SymPys internal implementation but perhaps
#26595 (redirect of #26593)
#26579
and this issue are connected in some way (missing or erroneous implementaion of cosh, sinh properties).