Упростите выражение[latex]sin ^{2} ( \frac{pi}{4}+a )-sin^{2} ( \frac{pi}{4}-a )[/latex]

[latex]\sin^2\bigg( \dfrac{\pi}{4} + \alpha \bigg)-\sin^2\bigg(\dfrac{\pi}{4} - \alpha \bigg)= \dfrac{1-\cos\bigg(\dfrac{\pi}{2} + \alpha \bigg)}{2} - \dfrac{1-\cos\bigg(\dfrac{\pi}{2}- \alpha \bigg) }{2} =[/latex] [latex]= \dfrac{1-\cos\bigg(\dfrac{\pi}{2}+ \alpha \bigg) -1+\cos\bigg(\dfrac{\pi}{2}- \alpha \bigg)}{2} = \dfrac{\sin \alpha +\sin \alpha }{2} =\sin \alpha [/latex]