Using the Pythagorean identity to verify an identity

The video tutorial explains how to use the Pythagorean identity to rewrite cosine in terms of sine. It begins by introducing the identity and then demonstrates solving for cosine. The instructor simplifies the expression by plugging in values and removing parentheses, ultimately verifying that the left side of the equation equals the right side.

Explain the process of simplifying the expression involving cosine and sine squared.

What conclusion can be drawn when the left side equals the right side in the equation?