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

• To: mathgroup at smc.vnet.net
• Subject: [mg3430] Re: [mg3402] How to force ( Exp[I x]/2+Exp[-I x]/2=cos(x) ) ?
• From: Dave Snead <76300.3545 at compuserve.com>
• Date: Thu, 7 Mar 1996 02:23:15 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```yjtsai at leland.Stanford.EDU (Yeou-Jyh Tsai) writes

> 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

Try ComplexExpand; it assumes all variables are real.

In:= {Exp[I x]/2 + Exp[-I x]/2, I Exp[-I x]/2 - I Exp[I x]/2} //
ComplexExpand

Out= {Cos[x], Sin[x]}

Good Luck,