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Re: Question : How to force ( Exp[I x]/2+Exp[-I x]/2=cos(x) ) ?

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  • Subject: [mg3403] Re: Question : How to force ( Exp[I x]/2+Exp[-I x]/2=cos(x) ) ?
  • From: ianc (Ian Collier)
  • Date: Mon, 4 Mar 1996 02:34:44 -0500
  • Organization: Wolfram Research, Inc.
  • Sender: owner-wri-mathgroup at wolfram.com

In article <4hbgms$4uu at dragonfly.wolfram.com>, yjtsai at leland.Stanford.EDU
(Yeou-Jyh Tsai) wrote:

> Hello,
> 
>         I use Mathematica's MatrixExp to generate the symbolic form of
> a matrix's exponential. It gives me lots of
>           I x     -I x          -I x      I x
>          E      E            I E        IE
>         ---   + ------ and  -------- - -----
>          2         2            2        2
> which should be converted to Cos[x] and Sin[x], respectively. Does anyone
> know how to do this ? 
> 
> Thanks a lot!
> 
> Yeou-Jyh Tsai
> tsai at relgyro.stanford.edu

You can use the function ComplexToTrig, which is defined in
Algebra`Trigonometry`one of the standard packages distributed
with Mathematica. For example:

In[1]:=
    Needs[ "Algebra`Trigonometry`" ]

In[2]:=
    ComplexToTrig[ Exp[I x]/2+Exp[-I x]/2 ]

Out[2]=
    Cos[x] - I Sin[x]   Cos[x] + I Sin[x]
    ----------------- + -----------------
            2                   2

In[3]:=
    Together[ % ]
Out[3]=
    Cos[x]

I hope this helps.

--Ian

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Ian Collier
Wolfram Research, Inc.
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