Answer
See below.
Work Step by Step
$LHS=ln(|sec\theta+tan\theta|)(|sec\theta-tan\theta|)=ln|sec^2\theta-tan^2\theta|=ln1=0=RHS$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.