Re: Trig Simplifications

• To: mathgroup at smc.vnet.net
• Subject: [mg3704] Re: Trig Simplifications
• From: hohmuth at cipserv1.physik.uni-ulm.de (Lars Hohmuth)
• Date: Wed, 10 Apr 1996 02:10:51 -0400
• Organization: Uni Ulm
• Sender: owner-wri-mathgroup at wolfram.com

```In article <4ka54g\$sai at dragonfly.wolfram.com> Alexander Casti <arc at carmen.phys.columbia.edu> writes:
>From: Alexander Casti <arc at carmen.phys.columbia.edu>
To: mathgroup at smc.vnet.net
>Subject: Trig Simplifications
>Date: 8 Apr 1996 04:36:32 GMT

>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

If you have the Trigonometry package loaded, try the command
TrigToComplex[Cos[x] + I Sin[x]].

CU,

Lars

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