How to verify a trigonometric identity by expanding one side

The video tutorial discusses the complexity of a mathematical problem and explores different approaches to simplify it. The instructor decides to make the left side of the equation look like the right side and expands the tangent expression using the FOIL method. The process involves combining terms and simplifying the expression to reach the final result, which is verified using a reference sheet.

What conclusion can be drawn from the expression combined with tangent squared of X?

How does the expression 1 + tangent squared of X relate to secant squared X?