## anonymous 5 years ago csc α - sin α =cos α cot α How do I show that this is an identity?

1. anonymous

$\csc \alpha -\sin\alpha=\frac{1}{\sin\alpha}-\sin\alpha$ $=\frac{1-\sin^2\alpha}{\sin\alpha}$ $=\frac{\cos^2\alpha}{\sin\alpha}$ $\cos\alpha\frac{\cos\alpha}{\sin\alpha}$ $=\cos\alpha \cot\alpha$

2. anonymous

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

3. anonymous

Thank you ebbflo!

4. anonymous

HEYY how do u Find the number of possible 5-card hands that contain 4 spades and 1 card that is not a spade. the cards are taken from a standard 52 card deck.

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