Question

Перетворіть добуток у суму 2cos(a+b)cos(a-b) sin48°sin74° Sin(60°+a)sin(60°-a)

Answer 1

$1)2Cos(\alpha+\beta)Cos(\alpha-\beta)=2*\frac{1}{2}(Cos(\alpha+\beta-\alpha+\beta)+Cos(\alpha+\beta+\alpha-\beta))=Cos2\beta+Cos2\alpha$

$2)Sin48^{o}Sin74^{o}=\frac{1}{2}(Cos(48^{o} -74^{o})-Cos(48^{o}+74^{o} ))=\frac{1}{2}(Cos26^{o}-Cos122^{o})\\\\3)Sin(60^{o}+\alpha)Sin(60^{o}-\alpha)=\frac{1}{2}(Cos(60^{o} +\alpha-60^{o}+\alpha)-Cos(60^{o}+\alpha+60^{o}-\alpha))=\frac{1}{2}(Cos2\alpha-Cos120^{o})$