## Hannah_Ahn Group Title Prove the identity $\left( \cot \theta \over \sin \theta - \csc \theta \right) = -\sec \theta$ 2 years ago 2 years ago

1. satellite73 Group Title

first we do the algebra $\frac{\frac{a}{b}}{b-\frac{1}{b}}=\frac{a}{b^2-1}$

2. satellite73 Group Title

no replace a by cosine, b by sine and get $\frac{\cos(x)}{\sin^2(x)-1}=-\frac{\cos(x)}{1-\sin^2(x)}=-\frac{\cos(x)}{\cos^2(x)}=-\sec(x)$

3. Hannah_Ahn Group Title

$a \over b^2 - 1$ ?????

4. Hannah_Ahn Group Title

oooh gotcha. i thought that was the right side,

5. satellite73 Group Title

yes $\frac{\frac{a}{b}}{b-\frac{1}{b}}=\frac{a}{b^2-1}$ multiply top and bottom by $b$and get it in one step

6. Hannah_Ahn Group Title

thanks! :)