I have submitted a bug report.

A shorter example that fails the first time, in my Maple 2023.0:

restart;
expr := (x^2)^(1/2)/((x+y)*sqrt(x^2+1)+x^2*(1/2*y^2-1))^2:

simplify(expr);
Error, (in simplify/size/collect_and_recurse) invalid arguments to coeffs

In my Maple 2022.2 (64bit Linux) this example and the OP's worksheet run without error.

@MANUTTM What do you think that the plots of T1(i) and T2(i) might mean, about the relative sizes of t1 and t2 for any particular value of i ?

@MDD You could create a re-usable procedure (to handle the entries individually, via map, or which itself maps across F).

Such a procedure could accept a list of names, L, so that the sort could be done with plex(op(L)).

Let me know if you'd like the whole thing shown.

@MANUTTM When you examine your plot3d surface of the objective are you not considering the constraints (eg. eq4, eq5) on i and q? Otherwise, I don't understand what you mean by, "...and the answer from graph are different."

Could you explain your use of your eq6 constraint?

@C_R Why do you write it as , "new options" in the context of your example? Your smaller example works in many older versions.

How would you use your suggestion of convert (sincos and/or tan, etc) to handle the OP's original example to get a form as he expected?

@C_R I meant what I wrote in the first snippet, addressing the OP's actual example and literal query about cot(90 - alpha/2).

I wrote only the second snippet because I wasn't sure whether the "-90" was intentional (in radians).

@MANUTTM Why didn't you mention this goal at the beginning?

Why do you keep starting separate Question threads on the same underlying problem?

@MANUTTM I don't know what accuracy you'll be needing, both for the estimated roots as well as following substitution of such solutions into other expressions (or the original equation). You might need to adjust the working precision according to what you later do with the computed roots.

If you substitute values for i into K2 then its values may become very large (positive or negative) if you allow a wide a range for t2. And (as a function of t2) it can be very steep near the root, relative to when t2 is far from the root, which can make the numeric root-finding more difficult. By using a restricted range for t2 the root-finding process can do better.

@ludvigpujsek Sorry, I meant to write unapply, not unassign. Oof.

I'll correct it in my Answer.

@MANUTTM A different range is required for t2.

Download q3m_ac_t2.mw

@mmcdara Yes, and content also has a Help page, which can be directly queried.

The content command has been in Maple for a long time.

The rhs of sort's key option isn't necessarily part of only the sort command. It can be something more general; in this case another command.

It is a shame that the OP's original example is so vague. We cannot know from it even simple aspects such as whether the sign of the coefficient matters.

@mmcdara The key option is explained in the Description section of the sort Help page.

That option was available in Maple 16.02 (released 2012). I don't think of that as "recent". I don't recall when it first appeared.

@dharr From the Options subsection of the Description section of the rtable Help page (emphasis, mine):

"The fill value is only used to fill those elements of the rtable that are unspecified in spite of the indexing function. For instance, the fill value is not used to fill the lower triangle of an upper triangular Matrix. For a sparse rtable, the fill value is always ignored."

@mmcdara You are querying the address of the values assigned to the entries of V, ie. the address of whatever V[1],etc, evaluate to. Those are not addresses of part of the V structure itself.

The address of the name s is the same, regardless. And the same goes for 1.

I don't see how your answer, "it's more a problem of visualization than a problem of storage" might be meaningful here.

I don't see how your use of addressof is useful to understanding here.