Answer
See the steps.
Work Step by Step
$RHS = \tan{x} + \cot{x} = \dfrac{\sin{x}}{\cos{x}} + \dfrac{\cos{x}}{\sin{x}} = \dfrac{\sin^2 {x} + \cos^2 {x}}{\cos{x} \sin{x}}$
$RHS = \dfrac{1}{0.5 \sin{2x}} = 2 \csc{2x} = LHS$
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.