       Re: TrigReduce: controlling the scope

• To: mathgroup at smc.vnet.net
• Subject: [mg129068] Re: TrigReduce: controlling the scope
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Tue, 11 Dec 2012 19:54:37 -0500 (EST)
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• References: <20121211072505.3729568A2@smc.vnet.net>

```In:= expr2 = (expr1 =
Sin[alpha] Cos[omega tau1] Cos[omega tau2] Cos[beta] +
Cos[alpha] Cos[omega tau1] Cos[omega tau2] Sin[beta] +
Sin[alpha] Cos[omega tau1] Cos[omega tau2] Sin[beta] +
Cos[alpha] Cos[omega tau1] Cos[omega tau2] Cos[beta]) /.
f_[alpha] g_[beta] r_ :> f[alpha] g[beta] TrigReduce[r] //
Map[Simplify, #, {3}] & // Factor

Out= 1/2 (Cos[omega (tau1 - tau2)] +
Cos[omega (tau1 + tau2)]) (Cos[alpha] + Sin[alpha]) (Cos[beta] +
Sin[beta])

In:= expr1 == expr2 // Simplify

Out= True

Bob Hanlon

On Tue, Dec 11, 2012 at 2:25 AM, alan <alansbarnett at verizon.net> wrote:
> I have an expression that is a sum of products of trignometric functions. Each term is something like this:
> Sin[alpha] Cos[omega tau1] Cos[omega tau2] Cos[beta].                  (1)
> I want to apply trig identities to the terms that contain omega to transform them into trig functions of sums and differences, but I don't want the same transformation applied to the terms involving alpha and beta.  For example, I want to express (1) as
> (1/2) Sin[alpha] Cos[beta](Cos[omega(tau1 - tau2)]+Cos[omega(tau1 + tau2)])
>
> If I apply TrigReduce to (1), I get terms like
> Cos[omega tau1 - omega tau2 + alpha - beta].
> How do I restrict the action of TrigReduce to terms containing omega?
> (I can do a hybrid calculation by cutting and pasting the terms I want, but I'd rather not have to cut and paste by hand).
>
> Thanks.
>

```

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