How to use the difference of two squares to simplify a trig expression

The video tutorial explains how to transform cosine squared using trigonometric identities. It covers the identity of sine squared plus cosine squared equals one and demonstrates how to express cosine squared as one minus sine squared. The instructor warns against common mistakes, such as incorrect cancellations, and introduces the concept of the difference of squares to simplify expressions. The tutorial emphasizes the importance of recognizing patterns and using mathematical techniques to solve problems effectively.

What caution does the speaker give regarding canceling terms in the expression?

How does the speaker suggest students should approach the problem of transforming trigonometric identities?