Re: Rewriting of Trigonometric Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26835] Re: [mg26803] Rewriting of Trigonometric Functions
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 25 Jan 2001 01:13:15 -0500 (EST)
• References: <200101240918.EAA03580@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thomas Engelhardt wrote:
>
> 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

In[9]:= Sin[a]*Sin[b] // TrigReduce // InputForm
Out[9]//InputForm= (Cos[a - b] - Cos[a + b])/2

In[10]:=  Sin[a]^2 // TrigReduce // InputForm
Out[10]//InputForm= (1 - Cos[2*a])/2

Daniel Lichtblau
Wolfram Research

```

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