Trigonometry is a branch of mathematics that deals with the relationship between the lengths and angles of triangles. Trigonometric identities play a crucial role in simplifying trigonometric expressions and equations. In this article, we will explore and prove the trigonometry identity: [ \frac{1 + \sec(A)}{\sec(A)} = \frac{\sin^2 A}{1 - \cos A} ] This identity involves…