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Re: TraditionForm Appears to be Inconsistent

• To: mathgroup at smc.vnet.net
• Subject: [mg99576] Re: [mg99551] TraditionForm Appears to be Inconsistent
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 8 May 2009 00:16:53 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200905071040.GAA19666@smc.vnet.net>
• Reply-to: murray at math.umass.edu

Because, I presume, Mathematica knows that Cos[x] always has the same 
value as Sin[x + \[Pi]/2] no matter what x is; it evaluates both sides 
of that equation and then decrees the equation True.

But Mathematica seems cautious if, for example, you enter

   Cos[a + b I] + Sin[a + b I]

which it leaves unevaluated further.  Then if you enter, say,

   Exp[I \[Theta]]==Cos[\[Theta]]+I Sin[\[Theta]]/.\[Theta]->a+b I

then it returns the result without further evaluation.

uk.org.microserf at googlemail.com wrote:
> Hi
> 
> The Mathematica 7 documentation says that
> 
> TraditionalForm[Exp[I \[Theta]] == Cos[\[Theta]] + I Sin[\[Theta]]]
> 
> will display the expression in traditional form, and indeed it does.
> However, the following evaluates the expression and then displays True
> in traditional form:
> 
> TraditionalForm[Cos[x] == Sin[x + \[Pi]/2]]
> 
> Why is TraditionalForm behaving differently in these two apparently
> identical situations, and how can I get Mathematica to display this
> trigonometric identity in traditional form?
> 
> Thanks in advance
> 
> Chris
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • TraditionForm Appears to be Inconsistent
    • From: uk.org.microserf@googlemail.com