Derive the given equations by letting + = x and = y, which leads to = 1/2(x + y)

Derive the given equations by letting α + β = x and α − β = y, which leads to α = 1/2(x + y) and β = 1/2(x − y). The resulting equations are known as the factor formulas.

Use Eqs. (20.9) and (20.11) and the substitutions above to derive the equation

sinx - siny = 2 sin(x - y) cos(x + y) (20.18)