SOLUTION: How do I prove that {{{(1-cosx)/sinx = +- sqrt((cscx-cotx)/(cscx+cotx))}}}?

Algebra ->  Trigonometry-basics -> SOLUTION: How do I prove that {{{(1-cosx)/sinx = +- sqrt((cscx-cotx)/(cscx+cotx))}}}?      Log On


   

Question 1108163: How do I prove that %281-cosx%29%2Fsinx+=+%2B-+sqrt%28%28cscx-cotx%29%2F%28cscx%2Bcotx%29%29?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%281-cosx%29%2Fsinx+=+%2B-+sqrt%28%28cscx-cotx%29%2F%28cscx%2Bcotx%29%29
(1-2cos+cos^2)/sin^2 = (csc-cot)/(csc+cot)
(1-2cos+cos^2)/sin^2 = (1-cos)/(1+cos)
(1-2cos+cos^2)/sin^2 = (1-cos)^2/(1-cos^2)
(1-2cos+cos^2)/sin^2 = (1-cos)^2/sin^2
(1-2cos+cos^2) = (1-cos)^2
QED
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You prove it working on it, not by asking about it.
I prefer to change to sine and cosine.
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PS I've never seen an example where working only one side makes a difference.