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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: [mg73741] Re: showing an expression equal to 0
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Tue, 27 Feb 2007 05:45:42 -0500 (EST)
  • References: <errm70$8bp$1@smc.vnet.net><erug82$t6f$1@smc.vnet.net>

I really appreciate you response Sem!

Dimitris

=CF/=C7 Sem =DD=E3=F1=E1=F8=E5:
> 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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