How to evaluate the half angle of cosine when given a triangle

The video tutorial explains the half angle formula for cosine, focusing on when to use the positive or negative sign based on the angle's quadrant. It demonstrates finding the hypotenuse using the Pythagorean theorem and calculating cosine by simplifying fractions and rationalizing the denominator. The tutorial provides a step-by-step approach to solving similar problems.

What steps are involved in simplifying the expression for cosine using the half angle formula?

How do you rationalize the denominator in the final answer for the cosine calculation?