How to verify an identity by simplifying complex fractions

The video tutorial explains the relationship between cosine and sine as reciprocals and demonstrates how to convert cosine into secant using reciprocal identities. It further explores combining like terms and using common denominators to simplify complex fractions, emphasizing the importance of algebraic properties in solving such problems.

Explain the process of combining like terms in the context of trigonometric identities.

What is the significance of identifying a common denominator when working with trigonometric expressions?