Learn how to solve problems step by step online. Prove the trigonometric identity (1+csc(x))/sec(x)-cot(x)=cos(x). Starting from the left-hand side (LHS) of the identity. Combine all terms into a single fraction with \sec\left(x\right) as common denominator. Simplify -\cot\left(x\right)\sec\left(x\right) by applying trigonometric identities. Cancel like terms \csc\left(x\right) and -\csc\left(x\right).

Prove the trigonometric identity (1+csc(x))/sec(x)-cot(x)=cos(x)