Maybe you can do want you need with tellsimpafter:
(%i1) matchdeclare(x,true)$
(%i2) tellsimpafter(cosh(asinh(x)) , sqrt(x^2 + 1));
(%o2) [coshrule1,simp-%cosh]
(%i3) cosh(asinh(a));
(%o3) sqrt(a^2+1)
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>To: maxima at math.utexas.edu
>From: Jan Bessai <jan.bessai at tu-dortmund.de>
>Sent by: maxima-bounces at math.utexas.edu
>Date: 01/20/2008 11:17AM
>Subject: Feature request: cosh(asinh(x)) = sqrt(x^2+1)
>
>Hi,
>Maxima is able to differentiate asinh(x) correctly, but does not know
>the equation cosh(asinh(x)) = sqrt(x^2 + 1) (at least not in 5.13.0)
>which is usually needed to do that.
>Could you add it, please?
>Thanks,
> Jan
>
>cosh(asinh(x)) = sqrt(1 - sinh?(asinh(x))) = sqrt(1 - x?)
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