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 ==== [MESSAGE SEPARATOR] ====