## Hannah_Ahn prove the identity: $\left( \cot x - 1 \over 1 - \tan x\right) = \left( \csc x \over \sec x \right)$ 2 years ago 2 years ago

1. satellite73

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

2. satellite73

sorry that was right hand side

3. Hannah_Ahn

it's okay (-:

4. satellite73

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. Hannah_Ahn

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