1. The problem statement, all variables and given/known data Prove that sec^(2)(x/2) divided by 1 - tan^(2)(x/2) is sec x 2. Relevant equations Trig identities. 3. The attempt at a solution I used the identity: 1 + tan^2(x) = sec^2(x) I get for numerator: 1 + tan^2(x/2) I kept denominator same: 1 - tan^2(x/2) I get the impression (intuition?) that this can be solved in its current form. But then since i couldn't after a while, i just went on to expand tan^2(x/2) using the double angle formula to get expressions in terms of tan(x). It turned into something lengthy, so i doubt that i'm doing it right.