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MathGroup Archive 2005

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FullSimplify on Hyperbolic Functions

  • To: mathgroup at
  • Subject: [mg53383] FullSimplify on Hyperbolic Functions
  • From: carlos at
  • Date: Sat, 8 Jan 2005 23:02:47 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Obviously ArcCosh[1+b^2/2]=2 ArcSinh[b/2] if b>=0. Here are
4 variations on trying to show it by FullSimplify:

ClearAll[b];  r1=ArcCosh[1+b^2/2]; r2=2*ArcSinh[b/2];

ArcCosh[1 + b^2/2] - 2*ArcSinh[b/2]


ArcCosh[1 + b^2/2]^2 - 4*ArcSinh[b/2]^2

-4*Log[(b + Sqrt[4 + b^2])/2]^2 + Log[(2 + b*(b + Sqrt[4 + b^2]))/2]^2
Why only the second one works?

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