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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91799] How to simplify ArcCos[x/Sqrt[x^2+y^2]] to Pi/2-ArcTan[x/Abs[y]]?
  • From: Peng Yu <PengYu.UT at gmail.com>
  • Date: Mon, 8 Sep 2008 05:03:06 -0400 (EDT)

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.

Thanks,
Peng


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