DEPRECATED Understanding angle addition formulas

Problem

Prove the cosine angle-sum identity by labeling lengths and angles in this diagram.
Some of the proof has been done for you in pink. Notice that the cosine of an obtuse angle is negative, so it's not the length of a segment -- its opposite is the length of a segment.
Segment/Angle
Measure
  • start overline, B, D, end overline
  • start overline, B, C, end overline
  • start overline, O, E, end overline
  • angle, D, C, B
  • angle, C, B, D
  • sine, y, sine, x
  • start fraction, pi, divided by, 2, end fraction, minus, x
  • sine, y, sine, x, minus, cosine, x, cosine, y
  • x
  • sine, y