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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 ?
Thanks for your time.
Alex
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