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MathGroup Archive 2001

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RE: Rewriting of Trigonometric Functions

  • To: mathgroup at
  • Subject: [mg26827] RE: [mg26803] Rewriting of Trigonometric Functions
  • From: "David Park" <djmp at>
  • Date: Thu, 25 Jan 2001 01:13:09 -0500 (EST)
  • Sender: owner-wri-mathgroup at


"TrigReduce[expr] rewrites products and powers of trigonometric functions in
expr in terms of trigonometric functions with combined arguments."

1/2*(1 - Cos[2*a])

% // TrigReduce
Sin[a] Sin[b]
1/2*(Cos[a - b] - Cos[a + b])

David Park
djmp at

> From: Thomas Engelhardt [mailto:thomas-a.engelhardt at]
To: mathgroup at
> 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

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