showing an expression equal to 0

*To*: mathgroup at smc.vnet.net*Subject*: [mg73719] showing an expression equal to 0*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sun, 25 Feb 2007 04:41:44 -0500 (EST)

Consider In[87]:= expr = ArcTan[y/Sqrt[R^2 - y^2]] - ArcSin[y/R]; The expression for R>0 and -R<y<R is equal to zero In[72]:= (Plot[Chop[Evaluate[expr /. R -> #1]], {y, -#1, #1}, Axes -> False, Frame -> True] & ) /@ Range[5] Based on Andrzej's resposnse on a recenet message I am able to show this equality for given R. E.g. for R=4 the following demonstrates that expr is equal to zero In[99]:= Simplify[expr /. R -> 4 /. y -> 2] Out[99]= 0 In[97]:= D[expr /. R -> 4, y] Factor[%] Out[97]= -(1/(4*Sqrt[1 - y^2/16])) + (y^2/(16 - y^2)^(3/2) + 1/Sqrt[16 - y^2])/ (1 + y^2/(16 - y^2)) Out[98]= 0 However not specifying R (but assuming R>0&&-R<y<R) I am not able to show that expr is equal to zero. Any ideas? Thanks!

**Follow-Ups**:**Re: showing an expression equal to 0***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>