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Re: Trignometric rules

  • To: mathgroup at smc.vnet.net
  • Subject: [mg118199] Re: Trignometric rules
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sat, 16 Apr 2011 07:34:22 -0400 (EDT)
  • References: <io6d3h$drj$1@smc.vnet.net> <io8tn0$qam$1@smc.vnet.net>

Am 15.04.2011 09:56, schrieb Peter Pein:
> Am 14.04.2011 11:00, schrieb Chelly:
>> I have an expression as hsown below
>>
>> tt = -4 k1^2 v^2 \[Epsilon]1^2 \[Epsilon]c^2 Cos[2 d1 + d2 + d3] -
>>      2 k1 k2 u^2 \[Epsilon]1 Cos[d1 + d2 - \[Phi]b - \[Phi]r] +
>>      2 k1^2 v^2 \[Epsilon]1^2 \[Epsilon]c^2 Cos[
>>        2 d1 + d2 + d3 - \[Phi]b - \[Phi]r] +
>>      2 k1^3 k2 v^2 \[Epsilon]1^3 \[Epsilon]c^2 Cos[
>>        d1 + d3 + \[Phi]b + \[Phi]r] +
>>      2 k1^2 u^2 \[Epsilon]1^2 Cos[2 d1 + d2 + d3 + \[Phi]b + \[Phi]r] -
>>      2 k1^2 v^2 \[Epsilon]1^2 \[Epsilon]c^2 Cos[
>>        2 d1 + d2 + d3 + \[Phi]b + \[Phi]r];
>>
>> I'd like to replace any term containing Cos[+/- phib + x_]  with 2 Sin [+/-phib] Sin[x]. How do I go about doing it.
>>
>> Thanks
>> Chelly
>>
>
> Hi Chelly,
>
> use pattern matching:
>
> tt /. Cos[pb:(s_. \[Phi]b /; Abs[s] == 1) + x_.] :>  2 Sin[pb] Sin[x]
>
> Peter
>

Oops! Of course:

tt /. Cos[pb:(s_. \[Phi]b /; Abs[s] == 1) + x_.] :>  2 Sin[s pb] Sin[x]

sorry,
Peter


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