两角和的正弦公式：几何与三角函数的结合 by zhang hongwei

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → O
2. Circle(O, 1 / 2) → c
3. Point(c) → A
4. Intersect(c, Line[O, A], 2) → B
5. Segment(A, B) → g
6. Point(c) → C
7. Segment(A, C) → h
8. Segment(B, C) → i
9. Line(C, y = 0) → f
10. Intersect(OrthogonalLine[A, f], f) → D
11. Intersect(OrthogonalLine[B, f], f) → E
12. Intersect(Line[B, f], OrthogonalLine[A, f]) → F
13. Segment(B, E) → j
14. Segment(B, F) → k
15. Segment(D, F) → l
16. Segment(D, E) → m
17. Angle(D, C, A) → α
18. Angle(C, B, A) → β
19. Angle(E, B, C) → γ
20. Angle(F, A, B) → δ
21. Angle(A, C, B) → ε
22. Angle(B, F, D) → ζ
23. Angle(F, D, E) → η
24. Angle(D, E, B) → θ
25. Text("1", Midpoint[A, B] + (0, -0.05)) → text1
26. Text(RotateText["\purple{\cos(α+β)}", 90°], F - (1 / 4 * (F - A)), true, true) → text2
27. Text("\purple{\sin(α+β)}", Midpoint[B, F] + (-0.08, 0.05), true, true) → text3
28. Text("$\red{\sin(α)}\blue{\cos(β)}$", E + (0.02, 0), true, true) → text4
29. Text("\red{\cos(α)}\blue{\sin(β)}", Midpoint[C, D] + (-0.06, 0), true, true) → text5