Re: Trigonometric simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg68888] Re: [mg68838] Trigonometric simplification
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Tue, 22 Aug 2006 05:20:25 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```They're not equal.

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

Plot[{r,Cos[a]*Sin[a]^2},{a,0,2Pi},PlotStyle->{Blue,Red}];

Simplify[r//TrigReduce,Element[a, Reals]]

Sin[a]^2/Abs[Sec[a]]

FullSimplify[r//TrigToExp,Element[a, Reals]]

Cos[a]*Sign[Sec[a]]*Sin[a]^2

Bob Hanlon

> 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.
>

```

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