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MathGroup Archive 2007

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Re: showing an expression equal to 0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73722] Re: showing an expression equal to 0
  • From: "Sem" <sarner2006-sem at yahoo.it>
  • Date: Mon, 26 Feb 2007 06:16:31 -0500 (EST)
  • References: <errm70$8bp$1@smc.vnet.net>

Hi dimitris,
you could try these steps for example:

In[1]:= eq= ArcTan[y/Sqrt[R^2-y^2]]==ArcSin[y/R];
            assum={R>0&&-R<y<R};

In[2]:= eq1= Thread[TrigToExp[eq],Equal];

Above there are some useful rules for log transformations:
In[3]:= LogComb[expr_] :=
          expr//.{a_ Log[b_]\[RuleDelayed] Log[b^a],
      Log[a_]+Log[b_]\[RuleDelayed] Log[Simplify[a b]]};

In[4]:= Simplify[eq1, assum];

In[5]:= % // LogComb
Out[5]= True

HTH,
    S.

"dimitris" <dimmechan at yahoo.com>  news:errm70$8bp$1 at smc.vnet.net...
> 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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