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