Verifying a trigonometric identity with multiple steps

The video tutorial explains how to verify a trigonometric identity by simplifying one side of the equation. The instructor chooses the more complex side to simplify, converts terms to sines and cosines, and uses algebraic manipulation to match both sides of the identity. The process involves strategic decisions on which operations to apply and how to handle terms to achieve the desired result.

How does the teacher suggest to convert the terms to simplify the expression?

What does the teacher multiply the top and bottom of the fraction by?

What is the final expression that the teacher arrives at after simplification?