       Re: Rewriting of Trigonometric Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26858] Re: [mg26803] Rewriting of Trigonometric Functions
• From: "Carl K. Woll" <carlw at u.washington.edu>
• Date: Fri, 26 Jan 2001 01:27:12 -0500 (EST)
• References: <200101240918.EAA03580@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thomas,

Try using the command TrigReduce, as in

TrigReduce[Sin[a]Sin[b]]

Cos[a - b] - Cos[a + b]
-----------------------
2

Carl Woll
Physics Dept
U of Washington

----- Original Message -----
From: "Thomas Engelhardt" <thomas-a.engelhardt at t-online.de>
To: mathgroup at smc.vnet.net
Subject: [mg26858] [mg26803] Rewriting of Trigonometric Functions

> 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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