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I would like to simplify the following expression

AAA (4 Sin[x]^2 Cos[x]^2) + AAA 4 Sin[x] Cos[x] + AAA

with the Trig->False option inside a Collect:

Collect[AAA (4 Sin[x]^2 Cos[x]^2) + AAA 4 Sin[x] Cos[x] + AAA, AAA, Simplify]

how can I insert the Trig->False condition in such an expression?

Thank you in advance

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FullSimplify[AAA (4 Sin[x]^2 Cos[x]^2) + AAA 4 Sin[x] Cos[x] + AAA] gives a simple form. I don't understand what you want to "collect". – bill s Feb 14 '14 at 15:48
this is just a simplified example. In this case the desired output is AAA (1 + 2 Cos[x] Sin[x])^2 and not the one returned by the code you suggested, which is AAA (Cos[x] + Sin[x])^4 – user9994 Feb 14 '14 at 15:54
It seems Trig -> False is in fact the default setting for that option ... Can you make it clear how you want to use this option with an example? This option does not appear in the code you posted. – Szabolcs Feb 14 '14 at 16:09
no, the default option is Trig->True in my Simplify: Options[Simplify, Trig] has as resultOut[4]= {Trig -> True}. I want to set Trig->True for the Simplify inside the Collect, as I asked in the main topic. The example is exactly the one above. Again, I would like the output AAA (1 + 2 Cos[x] Sin[x])^2. – user9994 Feb 14 '14 at 16:19
Either use SetOptions to change the default, or use Simplify[#, Trig -> False] & in the Collect – Simon Woods Feb 14 '14 at 16:27

As Simon Woods said in his comment, use the form

Collect[AAA (4 Sin[x]^2 Cos[x]^2) + AAA 4 Sin[x] Cos[x] + AAA, AAA, 
  Simplify[#, Trig -> False] &]
AAA (1 + 2 Cos[x] Sin[x])^2
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