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
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