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Rewriting of Trigonometric Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26803] Rewriting of Trigonometric Functions
• From: thomas-a.engelhardt at t-online.de (Thomas Engelhardt)
• Date: Wed, 24 Jan 2001 04:18:42 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Dear Mathgroup members,

I have just started to use Mathematica and directly ran into a problem:

I have rather lengthy expressions resulting from putting a sum of two
sinusodial swings to the power of three (Two-tone Intermodulation).
In order for me to recognise the contained frequencies I want Mathematica to
rewrite the contained Trigonometric functions in certain ways, namely like:

[sin(a)]^2  should be transformed into 1/2*(1+cos2x)
and for higher powers accordingly.

Furthermore:
sin(a)*sin(b) should be changed to 1/2*[cos(a-b) - cos(a+b)]

I have tried all kinds of "Expand" and "Trig..." operations but Mathematica
always keeps the powers on the trigonometric functions and doesn't change
the multiplications either.

Does anybody have an idea how I can get Mathematica to transform the
expressions in the desired way?

I appreciate your help!
Thanks in advance.

Kind Regards

Thomas
Munich, Germany

• Follow-Ups:
  • Re: Rewriting of Trigonometric Functions
    • From: "Carl K. Woll" <carlw@u.washington.edu>
  • Re: Rewriting of Trigonometric Functions
    • From: Daniel Lichtblau <danl@wolfram.com>