Answer
See below.
Work Step by Step
$LHS=\frac{1}{tan(\alpha-\beta)}=\frac{1+tan(\alpha)tan(\beta)}{tan(\alpha)-tan(\beta)}\times\frac{cot(\alpha)cot(\beta)}{cot(\alpha)cot(\beta)}=\frac{cot(\alpha)cot(\beta)+1}{cot(\beta)-cot(\alpha)}=RHS$
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.