       Re: Expanding Trig Power Identities

• To: mathgroup at smc.vnet.net
• Subject: [mg30365] Re: [mg30348] Expanding Trig Power Identities
• From: BobHanlon at aol.com
• Date: Sun, 12 Aug 2001 02:29:53 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2001/8/11 3:59:50 AM, adam_jurhs at xontech.com writes:

>How can I use Mathematica to find the expansion of various trigonometric
>power
>identities?  I've already tried TrigExpand w/o succes.
>
>I have functions of the form Sin[a](Sin[b])^n  and  Cos[a](Cos[b])^n
>where n is a power.
>
>I would like to get the fully expanded version of these functions, so
>that there are no more powers involved.  If n=1 then the answer is
>just the standard product relations that you can look up in the back
>of any trig book.  But I need to be able to do it for higher powers of
>n.  And I don't know how to even do it for n=1.
>

TrigReduce[Sin[a]*Sin[b]^3]

(1/8)*(-Cos[a - 3*b] + 3*Cos[a - b] - 3*Cos[a + b] +
Cos[a + 3*b])

Table[{y = Sin[a]*Sin[b]^n, "=", TrigReduce[y]}, {n, 4}] // TableForm

Table[{y = Cos[a]*Cos[b]^n, "=", TrigReduce[y]}, {n, 4}] // TableForm

Bob Hanlon
Chantilly, VA  USA

```

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