Prove the trigonometric identity $\cos\left(x\right)\sec\left(x\right)+\frac{-\cos\left(x\right)}{\sec\left(x\right)}=\sin\left(x\right)^2$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)sec(x)+(-cos(x))/sec(x)=sin(x)^2. Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \cos\left(\theta \right)\sec\left(\theta \right) = 1. Applying the trigonometric identity: \displaystyle\frac{1}{\sec(\theta)}=\cos(\theta). When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents.