csc α - sin α =cos α cot α How do I show that this is an identity?

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csc α - sin α =cos α cot α How do I show that this is an identity?

Mathematics
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\[\csc \alpha -\sin\alpha=\frac{1}{\sin\alpha}-\sin\alpha\] \[=\frac{1-\sin^2\alpha}{\sin\alpha}\] \[=\frac{\cos^2\alpha}{\sin\alpha}\] \[\cos\alpha\frac{\cos\alpha}{\sin\alpha}\] \[=\cos\alpha \cot\alpha\]
basic old trick, convert everything to sine (or cosine) then try to arrive at a Pythagorean identity in this case by rewriting with a common denominator then rewrite in the desired form
Thank you ebbflo!

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