Question

докажите тождество:4cosa cos(60°-a)cos(60°+a)=cos3a​

Answer 1

Решение во вложении...

Answer 2

Объяснение:

$4*cos\alpha *cos(60^0-\alpha )*cos(60^0+\alpha )=2*cos\alpha *(2*cos(60^0-\alpha )*cos(60^0+\alpha ))=\\=2*cos\alpha *(cos(60^0-\alpha +60^0+\alpha )+cos(60^0-\alpha -60^0-\alpha )=\\=2*cos\alpha *(cos120^0+cos(-2\alpha ))=2*cos\alpha *(cos(90^0+30^0)+cos2\alpha )=\\=2*cos\alpha *(-sin30^0+cos2\alpha )=-2*\frac{1}{2}*cos\alpha +2*cos2\alpha *cos\alpha =\\ =-cos\alpha +cos(2\alpha +\alpha )+cos(2\alpha -\alpha )=-cos\alpha +cos3\alpha +cos\alpha =cos3\alpha .$