Learn how to solve problems step by step online. Prove the trigonometric identity (sec(x)+tan(x)+-1)(1+sec(x)-tan(x))=2tan(x). Starting from the left-hand side (LHS) of the identity. Multiply the single term 1+\sec\left(x\right)-\tan\left(x\right) by each term of the polynomial \left(\sec\left(x\right)+\tan\left(x\right)-1\right). Simplify the product -(1+\sec\left(x\right)-\tan\left(x\right)). Simplify the product -(\sec\left(x\right)-\tan\left(x\right)).

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