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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.

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.

Calculus

Answers by Expert:

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.**Education/Credentials**

(See above.)