Re: Trigonometric simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg68881] Re: Trigonometric simplification
• Date: Tue, 22 Aug 2006 05:20:11 -0400 (EDT)
• References: <ecbnnc\$r29\$1@smc.vnet.net><ecc2pn\$ajl\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```> Hi Carlos,
>
> Using TrigReduce before Simplify will do it:
>
> r = Tan[a]^2/(Sec[a]^2)^(3/2);
> Simplify[TrigReduce[r], Assumptions -> {a > 0, Sec[a] > 0}]
>
> --> Cos[a]*Sin[a]^2
>
> Best regards,
> Jean-Marc

Thanks, that works perfectly.  Actually Sec[a]>0 as assumption
is sufficient. This is correct from the problem source, since
the angle is in the range (-Pi/2,Pi/2)

Here is a related question.  How can I get Mathematica to pass from

d = 2 + 3*Cos[a] + Cos[3*a]     (* leaf count 10 *)

to

1 + 2*Cos[a]^3                  (* leaf count 8 *)

TrigExpand[d] gives

2 + 3*Cos[a] + Cos[a]^3 - 3*Cos[a]*Sin[a]^2

Applying Simplify to that yields  2 + 3*Cos[a] + Cos[3*a]  so we are
back to the beggining.

```

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