Learn how to solve problems step by step online. Prove the trigonometric identity 1/(1+-1/(1+-1/(1-sec(x)^2)))=sec(x)^2. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: -\sec\left(\theta \right)^2+1=-\tan\left(\theta \right)^2. Simplify the fraction \frac{-1}{-\tan\left(x\right)^2} by -1. Combine all terms into a single fraction with \tan\left(x\right)^2 as common denominator.

Prove the trigonometric identity 1/(1+-1/(1+-1/(1-sec(x)^2)))=sec(x)^2