Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (1-csc(x)^2)/(cos(x)^2)=-csc(x)^2. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: 1-\csc\left(\theta \right)^2=-\cot\left(\theta \right)^2. Since \cos is the reciprocal of \sec, \frac{-\cot\left(x\right)^2}{\cos\left(x\right)^2} is equivalent to -\cot\left(x\right)^2\sec\left(x\right)^2. Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}.

Prove the trigonometric identity (1-csc(x)^2)/(cos(x)^2)=-csc(x)^2