Is This Solution Correct? Comparing My Answer to the Textbook's Solution

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I solved this question a bit differently from the textbook's solution manual and got a very different answer. I am wondering if this solution is sound? Thanks.
 

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Well you can always check yourself by differentiating your answer. However, on the last line (cot^2 x * sinx) is not equal to cotx * csc x.
 
I like the first line. I'ma try that next time and get wowz.
 

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