Re: Trigonometric simplification
- To: mathgroup at smc.vnet.net
- Subject: [mg68881] Re: Trigonometric simplification
- From: carlos at colorado.edu
- 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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