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

*To*: mathgroup at smc.vnet.net*Subject*: [mg120501] Re: Simplify[ArcTan[Tan[a] + Tan[b]]]*From*: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>*Date*: Tue, 26 Jul 2011 07:07:24 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j0jk6s$ovj$1@smc.vnet.net>

On Mon, 25 Jul 2011 12:31:40 +0100, rych <rychphd 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 It can certainly tell you something: In[1] := f = Function[{expr}, 100 Count[expr, _Tan, {0, Infinity}] + 100 Count[expr, _ArcTan, {0, Infinity}] + LeafCount[expr] ]; In[2] := FullSimplify[ ArcTan[Tan[a] + Tan[b]], ComplexityFunction -> f ] Out[2] = 1/2 I (Log[1-I Sec[a] Sec[b] Sin[a+b]]-Log[1+I Sec[a] Sec[b] Sin[a+b]]) However, this result is arguably neither interesting nor useful. Best, O. R.