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Re: How Expand?

• To: mathgroup at smc.vnet.net
• Subject: [mg127845] Re: How Expand?
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Sun, 26 Aug 2012 02:52:23 -0400 (EDT)
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On 24/08/2012 10:08, 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.
>
I addition to the comments of others, I would like to add, that if you 
simply want to check an identity, it is easier to use:

In[9]:= ( 1 + Cos[x] + I Sin[x] )^3==8 Cos[x/2]^3 (Cos[3x/2]+ I 
Sin[3x/2])//Simplify

Out[9]= True

(I.e. simplifying the assertion that the LHS == RHS, comes back with True)

This works in many situations in which it is extremely hard to force 
Mathematica to come up with a desired transformation spontaneously.

David Bailey
http://www.dbaileyconsultancy.co.uk