SOLUTION: Prove the following trigonometric identity: (sin(x))/(1-cos(x)) + (1-cos(x))/(sin(x)) = 2csc(x)

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Question 860032: Prove the following trigonometric identity:
(sin(x))/(1-cos(x)) + (1-cos(x))/(sin(x)) = 2csc(x)

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!


LHS
%28sin%28x%29%29%2F%281-cos%28x%29%29+%2B+%281-cos%28x%29%29%2F%28sin%28x%29%29
LCM of denominator
(1-cos(x)(sin(x))
we get +%28sin%5E2%28x%29%2B%281-cos%28x%29%29%5E2%29%29/%28%281-cos%28x%29%29%2A%28sin%28x%29%29%29

(sin^2(x)+1-2cos(x)+cos^2(x))/((1-cos(x)*sin(x))

(2-2cos(x))/((1-cos(x)*sin(x))
2(1-cos(x))/(1-cos(x)*sin(x))
=2/sin(x)
=2csc (x)
= RHS