For Math Geeks Only

For the math geeks among you, let’s try to prove the identities

cos(α + β) = cos α cos β − sin α sin β

sin(α + β) = sin α cos β + cos α sin β.

that we used in Section 2.1.4. Actually, I’m going to do the first one carefully and leave the second one for you, and I’m only going to do it in the first quadrant, that is, the case where α + β ≤ 90^◦. The following elegant geometric proof is from [Smiley 99]. ¹