Re: Trigonometric simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg68889] Re: [mg68838] Trigonometric simplification
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 22 Aug 2006 05:20:27 -0400 (EDT)
• References: <200608210727.DAA27449@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 21 Aug 2006, at 09:27, carlos at colorado.edu wrote:

> As an intermediate result of some calculations I have
> the expression
>
>    r=Tan[a]^2/(Sec[a]^2)^(3/2)
>
> where a is real. How can I coerce Mathematica into
> simplifying that to
>
>    r=Cos[a]*Sin[a]^2
>
> Both Simplify and FullSimplify with assumptions on a
> fail to get the simpler form.
>

I would not be very happy if Mathematica did what you seem to want it
to do only under the assumptions that a is real since:

r = Tan[a]^2/(Sec[a]^2)^(3/2)

Assuming[Pi/2 < a < 3*(Pi/2), Simplify[r]]

(-Cos[a])*Sin[a]^2

On the other hand:

Assuming[-Pi/2 < a < Pi/2, Simplify[r]]

Cos[a]*Sin[a]^2

Andrzej Kozlowski

```

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