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Inverse Trig Functions

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Charles Hottel

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Nov 17, 2009, 10:27:05 PM11/17/09
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Here is a true or false problem:

(arcsin x)**2 + (arccos x)**2 = 1

I know that this is false and can prove it via a specific example, say with
x = 0.5

However I seem to be unable to come up with a generalized expression for the
left hand side of the equation that would also show that it is false. How
would you begin to develop such an expression. Thanks.


Virgil

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Nov 17, 2009, 10:53:19 PM11/17/09
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In article <h--dnS_UmqUe9J7W...@earthlink.com>,
"Charles Hottel" <cho...@earthlink.net> wrote:

What leads you to suppose that the left hand side can be made any
simpler that it already is?

Greg Neill

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Nov 17, 2009, 11:11:54 PM11/17/09
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One contradictory example is sufficient proof.


Charles Hottel

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Nov 19, 2009, 7:46:10 AM11/19/09
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"Virgil" <Vir...@home.esc> wrote in message
news:Virgil-4654F7....@bignews.usenetmonster.com...

Well all of the other problems in this section use the regular trig
functions and trigonometric identities to get rid of the inverse functions
in order to develop the solution. Sort of like getting rid of arcsin x by
taking sin (arcsin x) to obtain x.


Virgil

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Nov 19, 2009, 2:01:41 PM11/19/09
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In article <YuydnZrhleKNo5jW...@earthlink.com>,
"Charles Hottel" <cho...@earthlink.net> wrote:

> "Virgil" <Vir...@home.esc> wrote in message
> news:Virgil-4654F7....@bignews.usenetmonster.com...
> > In article <h--dnS_UmqUe9J7W...@earthlink.com>,
> > "Charles Hottel" <cho...@earthlink.net> wrote:
> >
> >> Here is a true or false problem:
> >>
> >> (arcsin x)**2 + (arccos x)**2 = 1
> >>
> >> I know that this is false and can prove it via a specific example, say
> >> with
> >> x = 0.5
> >>
> >> However I seem to be unable to come up with a generalized expression for
> >> the
> >> left hand side of the equation that would also show that it is false.
> >> How
> >> would you begin to develop such an expression. Thanks.
> >
> > What leads you to suppose that the left hand side can be made any
> > simpler that it already is?
>
> Well all of the other problems in this section use the regular trig
> functions and trigonometric identities to get rid of the inverse functions
> in order to develop the solution. Sort of like getting rid of arcsin x by
> taking sin (arcsin x) to obtain x.

But if you can already prove the given statement false by citing a
specific counterexample, there is no need for anything further.

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