## anonymous 4 years ago prove the identity: $\left( \cot x - 1 \over 1 - \tan x\right) = \left( \csc x \over \sec x \right)$

1. anonymous

left hand side is $\frac{\frac{1}{b}}{\frac{1}{a}}=\frac{a}{b}$

2. anonymous

sorry that was right hand side

3. anonymous

it's okay (-:

4. anonymous

left hand side is $\frac{\frac{a}{b}-1}{1-\frac{b}{a}}=\frac{a^2-ab}{ab-b^2}=\frac{a(a-b)}{b(a-b)}=\frac{a}{b}$ so there are the same. there is no trig here

5. anonymous

that is an awesome way to prove it! you are amazing! thanks!!!