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Topic: Proving trigonometric identities
Replies: 32   Last Post: Jan 27, 2009 1:59 AM

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Angus Rodgers

Posts: 1,683
Registered: 7/16/07
Re: Proving trigonometric identities
Posted: Jan 23, 2009 6:32 AM
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On Fri, 23 Jan 2009 00:41:45 -0800 (PST), Albert
<albert.xtheunknown0@gmail.com> wrote:

>This (I think) is the last trig proof I've to do (there may be some in
>the next booklet though):
>
>(tan x + sec x - 1) / (tan x - sec x + 1) = (1 + sin x) / cos x
>
>I've tried turning the tan and sec into sin and cos but I can't
>factorise the resulting fraction down to a denominator of cos x. Also,
>I've tried rationalising the fraction but it can't be simplified.
>What's a key idea I should consider to tackle this proof?


Another quick way to do this one (but still perhaps not the best
way) is to rewrite the RHS as tan x + sec x (which, even though
it looks less "elementary", at least vaguely matches the LHS), so
that you are left with proving:

tan x + sec x - 1 = (tan x + sec x)(tan x - sec x + 1)

which should not give too much trouble.

--
Angus Rodgers


Date Subject Author
1/20/09
Read Proving trigonometric identities
Albert
1/20/09
Read Re: Proving trigonometric identities
Angus Rodgers
1/20/09
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Albert
1/20/09
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Angus Rodgers
1/20/09
Read Re: Proving trigonometric identities
Albert
1/20/09
Read Re: Proving trigonometric identities
Angus Rodgers
1/20/09
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Angus Rodgers
1/20/09
Read Re: Proving trigonometric identities
Guest
1/20/09
Read Re: Proving trigonometric identities
Angus Rodgers
1/20/09
Read Re: Proving trigonometric identities
Albert
1/20/09
Read Re: Proving trigonometric identities
Angus Rodgers
1/20/09
Read Re: Proving trigonometric identities
matt271829-news@yahoo.co.uk
1/21/09
Read Re: Proving trigonometric identities
Albert
1/21/09
Read Re: Proving trigonometric identities
adder
1/21/09
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matt271829-news@yahoo.co.uk
1/23/09
Read Re: Proving trigonometric identities
Albert
1/23/09
Read Re: Proving trigonometric identities
Angus Rodgers
1/23/09
Read Re: Proving trigonometric identities
Angus Rodgers
1/23/09
Read Re: Proving trigonometric identities
Passerby
1/23/09
Read Re: Proving trigonometric identities
Dave Dodson
1/24/09
Read Re: Proving trigonometric identities
Albert
1/24/09
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Angus Rodgers
1/24/09
Read Re: Proving trigonometric identities
Albert
1/26/09
Read Re: Proving trigonometric identities
Albert
1/26/09
Read Re: Proving trigonometric identities
Driveby
1/26/09
Read Re: Proving trigonometric identities
Albert
1/26/09
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A N Niel
1/27/09
Read Re: Proving trigonometric identities
Albert
1/20/09
Read Re: Proving trigonometric identities
adder
1/20/09
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victor_meldrew_666@yahoo.co.uk
1/20/09
Read Re: Proving trigonometric identities
Dave Dodson
1/20/09
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Pfsszxt@aol.com
1/20/09
Read Re: Proving trigonometric identities
Albert

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