SOLUTION: Please prove the following trigonometric identity: [(1-cos(a))/(sin(a)] + [sin(a)/(1-cos(a))] = 2csc(a) Thank you for your time! It is much appreciated!

Question 441151: Please prove the following trigonometric identity:
[(1-cos(a))/(sin(a)] + [sin(a)/(1-cos(a))] = 2csc(a)
Thank you for your time! It is much appreciated!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Please prove the following trigonometric identity:
[(1-cos(a))/(sin(a)] + [sin(a)/(1-cos(a))] = 2csc(a)
..
Start with left side
[(1-cos)/(sin)]+[(sin)/(1-cos)]
LCD:sin(1-cos)
(1-cos)^2)+(sin^2)/sin(1-cos)
(1-2cos+cos^2+sin^2)/sin(1-cos)
Identity:sin^2+cos^2=1
(2-2cos)/sin(1-cos)
2(1-cos)/sin(1-cos)
2/sin=2csc
left side=right side
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