A trig identity that Mathematica doesn't know?

*To*: mathgroup at smc.vnet.net*Subject*: [mg22172] A trig identity that Mathematica doesn't know?*From*: Gianluca Gorni <gorni at dimi.uniud.it>*Date*: Thu, 17 Feb 2000 01:24:03 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello! The expression expr = ArcTan[ y/Sqrt[R^2-y^2] ] - ArcSin[ y/R ] should be identically zero when -R<y<R, as you can see with a simple drawing. Still Mathematica's FullSimplify[] does not seem to know about it: FullSimplify[ expr , {R>0, -R<y<R} ] returns expr with just a minor change. It works as expected for R=1, but not for R=2 or R=3. I met this example when I tried the integral Integrate[ Sqrt[R^2-y^2], y ] and saw that the result was more complicated than what you get from standard tables. I am using Mathematica 4. Gianluca Gorni -- +---------------------------------+ | Gianluca Gorni | | Universita` di Udine | | Dipartimento di Matematica | | e Informatica | | via delle Scienze 208 | | I-33100 Udine UD | | Italy | +---------------------------------+ | Ph.: (39) 0432-558422 | | Fax: (39) 0432-558499 | | mailto:gorni at dimi.uniud.it | | http://www.dimi.uniud.it/~gorni | +---------------------------------+