Question

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

Answer 1

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

Answer 2

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

Answer 3

Thank you ebbflo!

Answer 4

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.