When deriving the Sum to Product Identities for Sine and Cosine of (a + b) (a - b) we take X= (a + b) and Y = (a - b) and then ÷ by 2 when adding X + Y and X - Y. Is this because we have two values of a and b? When we are given say Sine of 105 degrees and 15 degrees we just add them and then take the difference rather than (a + b) + (a - b) and (a + b) - (a - b). We still divide by 2. Why is this?