Question

Перетворіть добуток у суму
Sin5a cos 3a
Sin (π/6+a)sin(π/6-a)

Answer 1

$1)Sin5\alpha Cos3\alpha=\frac{1}{2}(Sin(5\alpha-3\alpha)+Sin(5\alpha+3\alpha))=\frac{1}{2}(Sin2\alpha+Sin8\alpha)\\\\2)Sin(\frac{\pi }{6}+\alpha)Sin(\frac{\pi }{6}-\alpha)=\frac{1}{2}(Cos(\frac{\pi }{6}+\alpha-\frac{\pi }{6}+\alpha) -Cos(\frac{\pi }{6}+\alpha+\frac{\pi }{6}-\alpha))=\frac{1}{2}(Cos2\alpha-Cos\frac{\pi }{3})=$$=\frac{1}{2}(Cos2\alpha-\frac{1}{2})=\frac{1}{2}Cos2\alpha-\frac{1}{4}$