Evaluate the half angle for cosine from a triangle

The video tutorial explains the cosine formula and its application using triangles and constraints. It discusses how to determine the cosine value based on the quadrant and provides methods to simplify the expression. The tutorial emphasizes algebraic manipulation and rationalization of denominators to achieve a simplified form.

Explain the process of rationalizing the denominator in the context provided.

What is the final simplified form of the expression discussed in the text?