Verifying an identity by combining like terms and using reciprocal properties

The video tutorial guides viewers through solving a trigonometric equation by simplifying one side using trigonometric identities. The instructor begins by discussing the problem and deciding which side to work on. They then apply trigonometric and Pythagorean identities to simplify the equation, ultimately verifying the solution by ensuring both sides are equivalent. The process emphasizes strategic problem-solving and the application of fundamental trigonometric concepts.

How does one apply Pythagorean identities in this context?

What is the final expression derived from the equation, and how is it verified?