Question

Условие и вопрос на рисунке!!!!!!!

Answer 1

Объяснение:

$\left \{ {{cos\alpha +cos\beta =c} \atop {sin\alpha +sin\beta =s}} \right.\ \ \ \ \left \{ {{(cos\alpha +cos\beta )^2=c^2} \atop {(sin\alpha +sin\beta)^2 =s^2}}\ \ \ \ \left \{ {cos^2\alpha +2*cos\alpha *cos\beta +cos^2\beta =c^2} \atop {sin^2\alpha +2*sin\alpha *sin\beta +sin^2\beta =s^2}} \right. .$

Суммируем эти уравнения:

$sin^2\alpha +cos^2\alpha +2*cos\alpha *cos\beta +2*sin\alpha *sin\beta +sin^2\beta +cos^2\beta =c^2+s^2\\1+2*cos\alpha *cos\beta +2*sin\alpha *sin\beta+1=c^2+s^2\\2+2*(cos\alpha *cos\beta +sin\alpha *sin\beta )=c^2+s^2\\2*cos(\alpha -\beta )=c^2+s^2-2\ |:2\\cos(\alpha -\beta )=\frac{c^2+s^2-2}{2} .$