Learn how to solve problems step by step online. Prove the trigonometric identity (tan(x)^2)/((sec(x)+1)^2)=(sec(x)-1)/(sec(x)+1). Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \tan\left(\theta \right)^2 = \sec\left(\theta \right)^2-1. Simplify \sqrt{\sec\left(x\right)^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Calculate the power \sqrt{1}.

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