       showing an expression equal to 0

• To: mathgroup at smc.vnet.net
• Subject: [mg73719] showing an expression equal to 0
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Sun, 25 Feb 2007 04:41:44 -0500 (EST)

```Consider

In:=
expr = ArcTan[y/Sqrt[R^2 - y^2]] - ArcSin[y/R];

The expression for R>0 and -R<y<R is equal to zero

In:=
(Plot[Chop[Evaluate[expr /. R -> #1]], {y, -#1, #1}, Axes -> False,
Frame -> True] & ) /@ Range

Based on Andrzej's resposnse on a recenet message I am able to show
this equality for
given R.

E.g. for R=4 the following demonstrates that expr is equal to zero

In:=
Simplify[expr /. R -> 4 /. y -> 2]

Out=
0

In:=
D[expr /. R -> 4, y]
Factor[%]

Out=
-(1/(4*Sqrt[1 - y^2/16])) + (y^2/(16 - y^2)^(3/2) + 1/Sqrt[16 - y^2])/
(1 + y^2/(16 - y^2))
Out=
0

However not specifying R (but assuming R>0&&-R<y<R) I am not able to
show that
expr is equal to zero.

Any ideas?

Thanks!

```

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