Re: How to simplify ArcCos[x/Sqrt[x^2+y^2]] to Pi/2-ArcTan[x/Abs[y]]?

*To*: mathgroup at smc.vnet.net*Subject*: [mg91834] Re: How to simplify ArcCos[x/Sqrt[x^2+y^2]] to Pi/2-ArcTan[x/Abs[y]]?*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Tue, 9 Sep 2008 06:59:03 -0400 (EDT)*References*: <ga2po2$p77$1@smc.vnet.net>

Peng Yu schrieb: > Hi, > > ArcCos[x/Sqrt[x^2+y^2]] > > and > > Pi/2-ArcTan[x/Abs[y]] > > are the same. > > But I can not get the first expression be simplified to the second > one. And the following command can not be simplified to zero in > mathematica as well. > > FullSimplify[ArcCos[x/Sqrt[x^2 + y^2]] - ( Pi/2 - ArcTan[x/Abs[y]]), > Element[x, Reals] && Element[y, Reals]] > > I'm wondering if there is any walkaround to do this simplification. Try Assuming[x > 0 && y > 0, FullSimplify[ TrigToExp[ArcCos[x/Sqrt[x^2 + y^2]] - (Pi/2 - ArcTan[x/Abs[y]])]]] (1/2)*I*(Log[1/(I*x + y)] + Log[I*x + y]) Obviously Mathematica isn't making a guess to which leaf of the complex Log your algebraic complex travel history brought even if you arrived on the positive real line. -- Roland Franzius

**Follow-Ups**:**Re: Re: How to simplify ArcCos[x/Sqrt[x^2+y^2]] to Pi/2-ArcTan[x/Abs[y]]?***From:*"Peng Yu" <pengyu.ut@gmail.com>