# Prevent FullSimplify from converting trigonometric expressions to exponential

There's an option for FullSimplify, which is Trig, and with it I could prevent a trigonometric identities from being used.

I'm looking for a similar option that would prevent FullSimplify from using the Euler formula

Sin[x] -> 1/2/I (Exp[x] - Exp[-x])
Cos[x] -> 1/2   (Exp[x] + Exp[-x])


So I want FullSimplify to retain Sin and Cos functions and to use trig identities, but no conversions to Exp.

### Edit

Example as requested from a comment:

Cos[2 B g t] Sin[u]^2 - I Sin[2 B g t] Sin[u]^2


In this formula, I want FullSimplify not to convert Cos[2 B g t] - I Sin[2 B g t] to Exp[-2IBgT].

• A small example that shows the problem you have? – Nasser Feb 22 '14 at 11:40
• @Nasser example given. – The Quantum Physicist Feb 22 '14 at 12:19
• Simplify[TrigReduce[s]] gives (Cos[2 B g t] - I Sin[2 B g t]) Sin[u]^2 but this might not generalize without more testing... – Nasser Feb 22 '14 at 12:25
• @Nasser This occurred to me actually, but is this as powerful as FullSimplify[] in everything? I mean I could probably need more functions that are not available in Simplify[]. – The Quantum Physicist Feb 22 '14 at 12:27

Given:

 expr = Cos[2 B g t] Sin[u]^2 - I Sin[2 B g t] Sin[u]^2


... one approach is:

 FullSimplify[expr, ExcludedForms -> {Cos[_], Sin[_]}]


(Cos[2 B g t] - I Sin[2 B g t]) Sin[u]^2

Another approach worth exploring is to use a custom ComplexityFunction, as per:

FF[ee_] := 1000 Count[ee, _Exp, {0, Infinity}] + LeafCount[ee]

FullSimplify[expr, ComplexityFunction -> FF]


Alas, the latter is not working as I might have expected, which is perhaps of interest in its own right.