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Re: Simplify[ArcTan[Tan[a] + Tan[b]]]

• To: mathgroup at smc.vnet.net
• Subject: [mg120495] Re: Simplify[ArcTan[Tan[a] + Tan[b]]]
• From: Gary Wardall <gwardall at gmail.com>
• Date: Tue, 26 Jul 2011 07:06:19 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j0jk6s$ovj$1@smc.vnet.net>

On Jul 25, 6:31 am, rych <rych... at gmail.com> wrote:
> Can't Mathematica tell anything about ArcTan[Tan[a] + Tan[b]]? Maybe
> there exists no useful identity for that? By useful I mean the
> expression with functions of the "angles" a and b other than tangents.
> Thanks
> Igor

Igor,

I'm not quite sure what you want Mathematica to do with it. It's not
like ArcTan and Tan are truly inverses.

ArcTan[Tan[W]]  my not be  W  while

Tan[ArcTan[W]] is  W.

Personally I think

ArcTan[Tan[a] + Tan[b]]

is simplified enough. Of course there are many alternate and equal
expressions to it that could be of some use. But, which one?

Gary