How to think through a verifying a trigonometric identity problem

The video tutorial explores solving trigonometric problems by choosing a side of the equation to work on and using trigonometric identities. The teacher initially attempts to simplify the expression using cosine and secant relationships but realizes the approach is not effective. After reassessing, a simpler method is used to arrive at the solution, demonstrating the importance of exploring different strategies in problem-solving.

What does the speaker mean by 'keeping them within the same family'?

What realization does the speaker have about the problem they are working on?

Describe the method the speaker uses to combine functions in the problem.