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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    \[\csc \alpha -\sin\alpha=\frac{1}{\sin\alpha}-\sin\alpha\] \[=\frac{1-\sin^2\alpha}{\sin\alpha}\] \[=\frac{\cos^2\alpha}{\sin\alpha}\] \[\cos\alpha\frac{\cos\alpha}{\sin\alpha}\] \[=\cos\alpha \cot\alpha\]

  2. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    Thank you ebbflo!

  4. anonymous
    • 5 years ago
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    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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