Trig Simplifications

• To: mathgroup at smc.vnet.net
• Subject: [mg3702] Trig Simplifications
• From: Alexander Casti <arc at carmen.phys.columbia.edu>
• Date: Mon, 8 Apr 1996 02:06:27 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```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 ?

Alex

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