Posted by Don on Saturday, December 17, 2011 at 6:50pm.
Here's where parentheses come in handy.
As written, the identity is wrong. What you meant to say was
(csc^3 - csc + cot)/csc
= (csc(csc^2 - 1) + cot)/csc
= (csc cot^2 + cot)/csc
= csc cot^2/csc + cot/csc
= cot^2 + cos/sin * sin
= cot^2 + cos
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