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Proving trigonometry identities

Posted on 2006-04-03
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Prove that   1  over 1-cosx   -      1 over 1+cosx  =   2cotxcscx
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Question by:jkk11
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by:
ozo earned 672 total points
ID: 16366558
1 /( 1-cosx)   -  1/( 1+cosx)
= (1+cosx)/((1+cosx)*(1-cosx)) - (1-cosx)/((1-cosx)*(1+cosx))
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by:Harisha M G
Harisha M G earned 664 total points
ID: 16367014
Hi,

1 /( 1-cosx)   -  1/( 1+cosx)
= (1 + cos x - 1 + cos x) / (1 - cos² x)
= 2cos x/sin² x
= 2(cos x/(sin x*sin x)
= 2(cos x/sin x)/sin x
= 2 tan x csc x

---
Harish
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LVL 27

Assisted Solution

by:BigRat
BigRat earned 664 total points
ID: 16369835
1 /( 1-cosx)   -  1/( 1+cosx)

=

(1+cosx) - (1-cosx) all divided by (1-cosx)(1+cosx)

The numerator is 2cosx, the denominator 1-cos²x = sin²x

as cosx/sinx is cotx and 1/sinx is cscx, we get 2cotxcscx.

Q.E.D

Quite Easily Done.

BTW: This question is NOT worth 500 points. It looks anyway like home work and ought to be reduce to 50 points.
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