Question

How do you prove the identity `(csc theta - 1) / cot theta = cot theta / (csc theta + 1)`?

Answer 1

`sin^2 A + cos^2 A = 1`
`1 + cot^2 A = csc^2 A`

`(csc theta - 1)/cot theta = ((csc theta - 1)(csc theta + 1))/(cot theta (csc theta + 1)) = (csc^2 theta - 1)/(cot theta (csc theta + 1)) = cot theta/(csc theta + 1)`