Visualization of Angle Addition Formulas

① This example dynamically demonstrates the geometric proofs of the sine and cosine angle addition formulas: sin(α+β)=sinα·cosβ+cosα·sinβ and cos(α+β)=cosα·cosβ−sinα·sinβ. ② Core mathematical concepts include trigonometric addition identities, definitions of sine and cosine, similarity of right triangles, and projection relationships. ③ Construction highlights: a unit circle is created with Circle; key points and segments are placed using Point and Segment; angles α and β are marked with Angle; perpendicular lines are drawn via OrthogonalLine; intersections are obtained with Intersect; and arcs are rendered with CircleArc. Objects such as O, c, A, B, C, D, E, F, G and derived lengths (sinαcosβ, cosαsinβ, etc.) illustrate each term of the formulas geometrically. ④ Suitable for high‑school trigonometry lessons, college pre‑calculus preparation, and as an interactive teaching aid for instructors or self‑study by students.