Re: Trig Simplifications

*To*: mathgroup at smc.vnet.net*Subject*: [mg3710] Re: Trig Simplifications*From*: Harald Berndt <haraldb at nature.berkeley.edu>*Date*: Wed, 10 Apr 1996 02:11:54 -0400*Organization*: University of California Forest Prodcts Lab*Sender*: owner-wri-mathgroup at wolfram.com

Alexander Casti 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] > I believe you don't really want what you've written out, because: Cos[x] + I Sin[x] - Cos[2 X] + I Sin[2 X] == Exp[I X] - Exp[- 2 I X]. That sign error is one part of the problem: one needs two replacement rules, Cos[t_]+I Sin[t_]-> Exp[I t] and Cos[t_]-I Sin[t_]-> Exp[-I t]. Using Pattern[t, Blank[]] (the t_) will take care of the different variable names x and 2 X, but there are still two substitutions required. One needs to use ReplaceRepeated[] (//.). Cos[x] + I Sin[x] + Cos[2 X] + I Sin[2 X]//.Cos[t_]+I Sin[t_]-> Exp[ I t] will work and so will Cos[x] + I Sin[x] - Cos[2 X] + I Sin[2 X]//.{Cos[t__]+I Sin[t__]-> Exp[I t], -(Cos[t_]-I Sin[t_])-> -Exp[- I t]} This still seems clumsy and I hope someone will suggest a more efficient way of writing this. -- ______________________________________________________________________ Harald Berndt, University of California Research Specialist Forest Products Laboratory Phone: 510-215-4224 FAX: 510-215-4299 ==== [MESSAGE SEPARATOR] ====