[tex]\displaystyle\bf\\\frac{Sin5\alpha -Sin3\alpha }{2Cos4\alpha } =\frac{2Sin\dfrac{5\alpha -3\alpha }{2} Cos\dfrac{5\alpha +3\alpha }{2} }{2Cos4\alpha } =\frac{2Sin\alpha Cos4\alpha }{2Cos4\alpha } =Sin\alpha[/tex]
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[tex]\displaystyle\bf\\\frac{Sin5\alpha -Sin3\alpha }{2Cos4\alpha } =\frac{2Sin\dfrac{5\alpha -3\alpha }{2} Cos\dfrac{5\alpha +3\alpha }{2} }{2Cos4\alpha } =\frac{2Sin\alpha Cos4\alpha }{2Cos4\alpha } =Sin\alpha[/tex]