Question

спростіть вираз cos4a*cos6a+cos2a+sin4a*sin6a

Answer 1

$Cos4\alpha*Cos6\alpha+Cos2\alpha +Sin4\alpha*Sin6\alpha=\\\\=(Cos4\alpha*Cos6\alpha+Sin4\alpha*Sin6\alpha)+Cos2\alpha=Cos(6\alpha-4\alpha)+Cos2\alpha=\\\\=Cos2\alpha+Cos2\alpha)=\boxed{2Cos2\alpha}$