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I can't seem to get FullSimplify to fully simplify this complicated expression. I've added relevant Assumptions that helped, but I still get this weird unnecessary reciprocal within a reciprocal that I'd expect Mathematica to catch easily. So, two questions:

How can I fix the specific problem with the reciprocal within a reciprocal?

Are there better coding techniques I could have used to, in general, get better results for this problem? I'm a bit rusty at Mathematica.

x = S/(Sin[q - theta/2]/Tan[phi] + Cos[q - theta/2]);
frac = x/(x /. phi -> theta);
phif = phi /. Solve[f == frac, phi][[1]];
phif = phif /. C[1] -> 0;
del = phif - (phif /. q -> Pi/2);
expr = D[del, f];
f0 = f /. Solve[expr == 0, f][[1]];

FullSimplify[f0, Assumptions -> {Sin[q + theta/2] > 0, Sin[q - theta/2] > 0}]
(* 1/2 Csc[2 q] Csc[theta/2] Sin[q] (-(1/Sqrt[(1/(-2 Cos[2 q] + 
   2 Cos[theta]))]) + 2 Sin[q + theta/2]) *)
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  • $\begingroup$ Also, sorry, I can't seem to get the code formatting to work here. Neither triple ticks before & after nor crtl-K are working. $\endgroup$
    – Jerry Guern
    Commented Dec 31, 2023 at 17:28
  • $\begingroup$ Apparently the formatting problem was because you started the previous two lines with "1:" and "2:" and that must have thought you were introducing some kind of list. Never seen that before. Removing those 4 characters and your formatting works fine. Strange. Now we can get to your real question $\endgroup$
    – Bill
    Commented Dec 31, 2023 at 17:30
  • $\begingroup$ @Bill Ah, thank you! $\endgroup$
    – Jerry Guern
    Commented Dec 31, 2023 at 17:31
  • $\begingroup$ And FullSimplify[f0, Assumptions->{Sin[q+theta/2]>0, Sin[q-theta/2]>0,-2Cos[2q]+2 Cos[theta]>0}] gets rid of your "stacked" rationals. Is that EXACTLY what you wanted? I am hoping that added assumption is actually true ;} $\endgroup$
    – Bill
    Commented Dec 31, 2023 at 17:33

1 Answer 1

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In response to Bill's helpful comments above, I started from scratch and just put in ALL of my assumptions, including those that were logically unnecessary or tighter than was logically necessary. This worked, and I learned an important lesson today.

f0 = FullSimplify[f0, Assumptions -> {q > theta, q < Pi - theta, theta > 0, theta < Pi/10}]
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