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Re: Trig Simplifications

  • To: mathgroup at
  • Subject: [mg3707] Re: Trig Simplifications
  • From: ianc (Ian Collier)
  • Date: Wed, 10 Apr 1996 02:11:22 -0400
  • Organization: Wolfram Research, Inc.
  • Sender: owner-wri-mathgroup at

In article <4ka54g$sai at>, Alexander Casti
<arc at> wrote:

> Basically my question is how to get mathematica to write
> Exp[I x] in place of Cos[x] + I Sin[x]
> Suppose I have the expression  
> In[1]: f[x_]= Cos[x] + I Sin[x] - Cos[2 X] + I Sin[2 X]
> I would like mathematica to simplify this into
> f[x_]= Exp[I X] - Exp[2 I X]
> I tried the substitution command
> In[2]: % ./ Cos[X]+I Sin[X]-> Exp[I X] and it returned
> Out[2]: E^{I X}  - Cos[2 X] + I Sin[2 X]
> So, it seems as though this simple minded approach is not
> enough for mathematica to understand the substitution rules
> for powers of complex exponentials other than the one I 
> explicitly gave.
> In addition, commands like Simplify[Blah] do not seem to do
> the trick either.  I believe I have the trigonometry package
> loaded in (via the command Needs["Algebra`Trigonometry`"]).
> What must I do ? 
> Thanks for your time.
> Alex

You can do this using the function TrigToComplex which
is defined in Algebra`Trigonometry`, one of the standard
packages distributed with Mathematica. Here is an example:

    Needs[ "Algebra`Trigonometry`" ]

    expr = Cos[x] + I Sin[x]
    Cos[x] + I Sin[x]

    TrigToComplex[ expr ]
      -I x    I x    -I x    I x
    -E     + E      E     + E
    ------------- + ------------
          2              2

     I x

This is documented in more detail on pages 15-17 of "The
Guide to Standard Mathematica Packages" Technical Report.

I hope this helps.


Ian Collier
Wolfram Research, Inc.
tel:(217) 398-0700   fax:(217) 398-0747    ianc at
Wolfram Research Home Page:


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