A “Proof by Picture” of the Angle Addition Formulas
All you need to know in order to follow the proof is:
- The basic trig identities:
- The center angle of the triangle is Θ.
- The hypotenuse is 1 (a radius of the unit circle).
- The side adjacent is cos Θ.
- The side opposite is sin Θ.
- The angle between the adjacent and opposite sides is a right angle.
- That any triangle can be scaled by a factor H:
- The angles stay the same.
- The sides are all multiplied by H.
- The hypotenuse in this example would become 1 × H = H.