How do you find the derivative of #sinthetacsctheta#?

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Answer 1 · 2016-12-09T14:51:38

This is a question partly to see whether you remember your trigonometry and partly to teach you that it's OK to rewrite before differentiating..

#csc theta = 1/sin theta#, so

#sin theta csc theta = 1#,

and the derivative is #0#

If you want to do more trigonometry , then use the product rule to get

#(cos theta) (csc theta) + (sin theta) (-csc theta cot theta)#.

Now simplify to get

#cot theta - cot theta = 0#.