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

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

In:= Simplify[eq1, assum];

In:= % // LogComb
Out= True

HTH,
S.

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

```

• Prev by Date: Re: conditional is giving wrong value
• Next by Date: Re: Re: Re: is 3?
• Previous by thread: Re: showing an expression equal to 0
• Next by thread: Re: showing an expression equal to 0