Re: simple question

• To: mathgroup at smc.vnet.net
• Subject: [mg73720] Re: simple question
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Mon, 26 Feb 2007 06:15:26 -0500 (EST)

```Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> Sorry, I posted not what I had intended. Let me do it all again. We
> define:
>
> I1 = Pi/2 - ArcTan[u];
> I2 = ArcTan[1/u];
>
> and want to show that I1==I2 for u>0. We check that the derivative of
> the difference is 0:
>
> In[42]:=
> FullSimplify[D[I1-I2,u],u>0]
>
> Out[42]=
> 0
>
> and not, to prove that I1==I2 for u>0 we simply need to evaluate the
> difference I1-I2 for just one suitable chosen u>0, e.g.
>
> FullSimplify[(I1-I2)/.u->1]
>
> 0

But one must be careful with that technique! Note that _everything_ above
still seems to work perfectly if the restriction u>0 is simply omitted
throughout, thereby seeming to show that Pi/2 - ArcTan[u] == ArcTan[1/u]
for _all_ u, which is, of course, false.

David

```

• Prev by Date: Re: deleting a title or subtitle in a notebook
• Next by Date: "movie" of Table output for web page
• Previous by thread: Re: simple question
• Next by thread: Re: simple question