Answer
See explanations.
Work Step by Step
Step 1. To prove the given identify, we need to prove $tan\theta+sec\theta-1=(tan\theta-sec\theta+1)(tan\theta+sec\theta)$
Step 2. Expand the right side to get $RHS=tan^2\theta-sec^2\theta+tan\theta+sec\theta=tan\theta+sec\theta-1=LHS$