Re: Rewriting of Trigonometric Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26847] Re: Rewriting of Trigonometric Functions
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Thu, 25 Jan 2001 01:13:25 -0500 (EST)
• References: <94m8st\$3mn@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thomas,

TrigReduce[Sin[x]^2]

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

TrigReduce[Sin[a]Sin[b]]

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

See File>Palettes>AlgebraicManipulation.
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Thomas Engelhardt" <thomas-a.engelhardt at t-online.de> wrote in message
news:94m8st\$3mn at smc.vnet.net...
> 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?
>
>
> Kind Regards
>
> Thomas
> Munich, Germany
>
>

```

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