Simpson's Formulas/Sine by Sine/Corollary 1

Corollary to Simpson's Formula for Sine by Sine

 * $\map \sin {A + B} \map \sin {A - B} = \paren {\sin A + \sin B} \paren {\sin A - \sin B} $

Proof
Set $\alpha = A + B$ and $\beta = A - B$ in Simpson's Formula for Sine by Sine

Before substitution:

After substitution: