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Re: How Expand?

• To: mathgroup at smc.vnet.net
• Subject: [mg127834] Re: How Expand?
• From: daniel.lichtblau0 at gmail.com
• Date: Sat, 25 Aug 2012 04:27:01 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
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• References: <k17g9n$dre$1@smc.vnet.net>

On Friday, August 24, 2012 4:08:07 AM UTC-5, news wrote:
> Hi folks,
> 
> 
> 
> How can I expand the following :
> 
> 
> 
> [ 1 + cos(x) + i sin(x) ]^3
> 
> 
> 
> to obtain;
> 
> 
> 
> 8 cos(x/2)^3 [cos(3x/2)+ i sin(3x/2)]
> 
> 
> 
> Thanks a lot.
> 
> 
> 
> Max.

This will come pretty close.

In[6]:= ee = 1+Cos[x]+I*Sin[x];

In[7]:= InputForm[TrigFactor[TrigExpand[ee]]]

Out[7]//InputForm= Cos[x/2]*(2*Cos[x/2] + (2*I)*Sin[x/2])

Daniel Lichtblau
Wolfram Research