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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[87]:=
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[72]:=
(Plot[Chop[Evaluate[expr /. R -> #1]], {y, -#1, #1}, Axes -> False,
Frame -> True] & ) /@ Range[5]
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[99]:=
Simplify[expr /. R -> 4 /. y -> 2]
Out[99]=
0
In[97]:=
D[expr /. R -> 4, y]
Factor[%]
Out[97]=
-(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[98]=
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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