Express sin(α+β)sin(α−β)\sin(\alpha + \beta)\sin(\alpha - \beta)sin(α+β)sin(α−β) using product-to-sum formulas.
sin2(α)cos2(β)\sin^2(\alpha)\cos^2(\beta)sin2(α)cos2(β)
cos2(β)−cos2(α)\cos^2(\beta) - \cos^2(\alpha)cos2(β)−cos2(α)
12[cos(2β)−cos(2α)]\frac{1}{2}[\cos(2\beta) - \cos(2\alpha)]21[cos(2β)−cos(2α)]
sin2(α)−sin2(β)\sin^2(\alpha) - \sin^2(\beta)sin2(α)−sin2(β)