• To: mathgroup at smc.vnet.net
• Subject: [mg71133] Re: Question about trig simplify
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 9 Nov 2006 03:37:43 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <eisgno\$ngg\$1@smc.vnet.net>

```Robert Pigeon wrote:
> Hello all,
> 	Is this a bug?
>
> 2*Sin[a]*Cos[a] // Simplify  gives Sin[2 a] as expected.
>
> But
>
> -2*Sin[a]*Cos[a] // Simplify  gives -2*Cos[a]*Sin[a]  ...... Why?
> If I do -2*(Sin[a]*Cos[a]) // Simplify I get the same answer.
>
> This comes from the rotation matrix: r = {{Cos[a],Sin[a]},{-Sin[a],Cos[a]}}.
> Then I do: r.r // Simplify. That gives: {{Cos[2 a],Sin[2 a]},{-2 Cos[a]
> Sin[a],Cos[2 a]}}. It does not matter if I do a FullSimplify instead of
> Simplify.
>
> After if I do r.r.r // Simplify. The answer is simplified correctly.
>
> I am using Mathematica 5.2 on Windows XP Home.
>
> Any idea?
>
> Robert
>
> Robert Pigeon
> TZ = -5
>
Try

TrigReduce[-2*Sin[a]*Cos[a]]

--> -Sin[2*a]

"TrigReduce[expr] rewrites products and powers of trigonometric
functions in expr in terms of trigonometric functions with combined
arguments."
See http://documents.wolfram.com/mathematica/functions/TrigReduce

Regards,
Jean-Marc

```

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