Trig Angle Addition Formulas

A “Proof by Picture” of the Angle Addition Formulas

Original proof by Sunny Snaith.

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.