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Calculus/Trigonometric Identities

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Hi,

Can you please help me prove that ((1-cosx)/(1+cosx))=(cscx-cotx)^2?

I can only do work on one side to prove that its end result is equal to the other side.

Thanks a lot.

Answer
Questioner:Manisha
Country:New Jersey, United States
Category:Calculus   <<<<<<<<< This belongs in the Advanced Math section
Private:No
Subject:Trigonometric Identities   <<< spelling fixed
Question:Hi,

Can you please help me prove that ((1-cosx)/(1+cosx))=(cscx-cotx)^2?

I can only do work on one side to prove that its end result is equal to the other side.

Thanks a lot.
-----------------------------------------
Actually, you are allowed to work on either or both sides, as long as you do them independently.  (No fair multiplying both sides by something, for example.)

But OK, work on the left side: (note abbreviations)
1 - c 1 - c
----- ----- =  <<<<<  RATIONALIZE
1 + c 1 - c

(1 - c)^2
--------- =   
1 - c^2

(1 - c)^2
--------- =  <<<<<< PYTHAGOREAN ID
 s^2

[ 1 - c ]^2
[-------] =
[  s    ]

[1/s - c/s ]^2

OK, take it from there.

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