Please Help problem

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4 total messages Started by Dimitris Sourmelidis Mon, 10 May 1999 00:00

Author: Dimitris Sourmelidis
Date: Mon, 10 May 1999 00:00

11 lines
1374 bytes

Guys here is a math prob!

if there is a triangle where : sin(�) * cos^3(�/2) = sin(�) * cos^3(�/2)
then we want to proof
that this triangle has two equal sides!


Please post a reply to xman@mypad.com


Thanks to any reply..

Re: Please Help problem

Author: Daniel Lichtman
Date: Mon, 10 May 1999 00:00

19 lines
1541 bytes

The two sides of the equation are equal!!
So it is always true!!
Daniel
Dimitris Sourmelidis <xman@mypad.com> a �crit dans le message :
373727b7@news3.us.ibm.net...
> Guys here is a math prob!
>
> if there is a triangle where : sin(�) * cos^3(�/2) = sin(�) * cos^3(�/2)
> then we want to proof
> that this triangle has two equal sides!
>
>
> Please post a reply to xman@mypad.com
>
>
> Thanks to any reply..
>
>
>

Re: Please Help problem

Author: Tomas
Date: Mon, 10 May 1999 00:00

30 lines
1871 bytes


Daniel Lichtman schreef:

> The two sides of the equation are equal!!
> So it is always true!!
> Daniel

I guess they aren't equal, though his nottation is rather ambiguous: � vs
�let's use A and B for notation:
his equation is:
sin(A) * cos^3(B/2) = sin(B) * cos^3(A/2)


> Dimitris Sourmelidis <xman@mypad.com> a �crit dans le message :
> 373727b7@news3.us.ibm.net...
> > Guys here is a math prob!
> >
> > if there is a triangle where : sin(�) * cos^3(�/2) = sin(�) * cos^3(�/2)
> > then we want to proof
> > that this triangle has two equal sides!
> >
> >
> > Please post a reply to xman@mypad.com
> >
> >
> > Thanks to any reply..
> >
> >
> >

Re: Please Help problem

Author: Richard Carr
Date: Mon, 10 May 1999 00:00

50 lines
2790 bytes

On Mon, 10 May 1999, Daniel Lichtman wrote:

:Date: Mon, 10 May 1999 22:17:44 +0200
:From: Daniel Lichtman <dlichtma@cybercable.fr>
:Newsgroups: can.schoolnet.math, can.schoolnet.math.jr, fj.sci.math,
:    fr.sci.maths, sci.math, uk.education.maths
:Subject: Re: Please Help problem
:
:The two sides of the equation are equal!!
:So it is always true!!
:Daniel
:Dimitris Sourmelidis <xman@mypad.com> a écrit dans le message :
:373727b7@news3.us.ibm.net...
:> Guys here is a math prob!
:>
:> if there is a triangle where : sin(Á) * cos^3(Â/2) = sin(Â) * cos^3(Á/2)

sin(A)=2sin(A/2)cos(A/2). Similarly for sin(B). Cancel cos(A/2) and
cos(B/2) and 2. We can do this as A,B can't be pi radians (180 degrees),
as we're in a triangle.
Hence sin(A/2)cos^2(B/2)=sin(B/2)cos^2(A/2).
Thus sin(A/2)-sin(B/2)=sin(A/2)sin^2(B/2)-sin(B/2)sin^2(A/2).
Hence either sin(A/2)=sin(B/2) or else 1=-sin(A/2)sin(B/2).
In the latter case we must have |sin(A/2)|=|sin(B/2)|=1, so A, B are odd
multiples of pi, a contradiction.
Thus the former situtation occurs.
Hence, A/2=B/2 or A/2+B/2=pi, whence A+B=2pi, a contradiction since
A+B<pi.
Thus A/2=B/2 and A=B. Thus the triangle has two angles (i.e. A,B) equal.
From this one can show the corresponding sides (i.e. a,b) are equal- see,
for example, Euclid Book 1, right near the start.

:> then we want to proof
:> that this triangle has two equal sides!
:>
:>
:> Please post a reply to xman@mypad.com
:>
:>
:> Thanks to any reply..
:>
:>
:>
:
:
:
:

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