SOLUTION: Simplify: (sec^2xcscx)/(sec^2x + csc^2x)

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Question 255277: Simplify:
(sec^2xcscx)/(sec^2x + csc^2x)
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify
(i) %28sec%5E2%28x%29%2Acsc%28x%29%29%2F%28sec%5E2%28x%29+%2B+csc%5E2%28x%29%29
turn everything into sin and cos as
(ii)
simplify the denominator to get
(iii)
Notice cos^2x + sin^2 x = 1. Multiply by the reciprocal to get
(iv) %28cos%5E2%28x%29%2Asin%5E2%28x%29%29%2F%28cos%5E2%28x%29%2Asin%28x%29%29
and simply
(v) sin%28x%29