Proving the Cosine Difference Identity Using the Distance Formula

This GeoGebra example demonstrates a geometric proof of the cosine difference identity cos(α-β)=cosαcosβ+sinαsinβ. It uses the distance formula on the unit circle to compute the length of a dotted segment in two different coordinate representations, then equates them to derive the identity. The construction involves commands such as Intersect to find circle-axis intersections, Segment to draw relevant segments, Point to mark vertices, Angle to display α and β, Rotate to create the difference angle, and a slider 'step' to animate the proof sequence. This resource is ideal for high school trigonometry or introductory college mathematics, helping learners visualize the geometric origin of the formula and strengthen their understanding of coordinate geometry and algebraic manipulation.