Sine and Cosine of Sum of Two Angles

① This example geometrically demonstrates the sine and cosine addition formulas: cos(A+B)=cosA·cosB−sinA·sinB and sin(A+B)=sinA·cosB+cosA·sinB. ② Core concepts include trigonometric addition identities, angle sum and difference, properties of parallelograms, and vector projection ideas. ③ Construction highlights: the sketch uses GeoGebra commands Line, Point, OrthogonalLine, Intersect, Segment, Polygon, Defined to create objects such as C_y, C_x, C, w, W, A_y, A_x, A, D, wa, wc, E, DE, AEC, AE_C, EC_A, CA, D', B, AB, BC, CD, showD, DA, showB, F, G, AGE, AG, GE, EA, EFA, EF, FA, AE_F, FC, F', showF, showG, H, forming a parallelogram and auxiliary lines that reveal the angle relationships. ④ Suitable for high‑school trigonometry lessons, college‑prep review, and introductory GeoGebra geometric construction workshops.