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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.

Start with the RHS:

(cscx-cotx)^2 = ( 1/sinx - cos x / sin x ) ^2 (change every function to sin and cosine)

= ((1-cos x )/sin x )^2 (same denominator, so we can add numerators)

= (1-cos x ) ^ 2/ (sin x)^2 (power distributes over division and multiplication )

= (1-cos x ) ^ 2/ ( 1 - (cos x)^2 ) (some trig identity that says sin^2 A + cos^2 A = 1)

= (1-cos x ) ^ 2/ ( 1 - cos x) (1+ cos x) (factor the denominator since it's

the difference of two squares.)

I leave it to you now to cancel simplify and finish it up. Happy holidays!

Calculus

Answers by Expert:

I can answer all calculus question. I am a Math Lecturer and I teach Math in a College, usually Calculus 1, Calculus 2 and Calculus 3 and Linear Algebra.

I have been teaching in this college for more than 12 years. Prior to that, I taught for three years as Visiting Assistant Professor.**Education/Credentials**

I got my doctorate from Univ. of Rochester in Algebraic Toppology. I got a MA from Univ of Rochester, an MA from York Univ. in Toronto and almost did my M.Sc in the National Univ. of Singapore.