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Mathematica

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  • $\begingroup$ It depends on your further intentions. You did not describe them and this makes it difficult to answer you. The intentions may be different. Suppose you only need to show a final result of your calculations containing Cos[I z]. Then use HoldForm[Cos[I z]] or Cos[HoldForm[I z]]. Another possibility is that you will make further analytical calculations, but for whatever reason want to keep Cos[I z] as it is. Then use Cos[i z] instead. On the very last stage of your calculations you may replace i by I as follows expression/.i->I. $\endgroup$ Commented Sep 30, 2021 at 12:49
  • $\begingroup$ Continuation: However, in this second case, I would not make tricks, but let Mathematica act in its natural way. One can always replace Cosh[z]->Cos[HoldForm[I z]] (and possibly alike replacements, if needed) after the calculations have been finished. $\endgroup$ Commented Sep 30, 2021 at 12:53
  • $\begingroup$ My intentions are to show the final result, I simply don't like it to be Cosh. The solution Cosh[z]->Cos[HoldForm[I z]] is appropriate, but I find very strange that some simplifications are controlled by "AutosimplifyTrigs" (like 1/Cos[z]) and others are not. Is there any reason for this? $\endgroup$ Commented Oct 3, 2021 at 1:21