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MathGroup Archive 2000

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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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