Question

Алгебра, 65 номер, ПОМОГИТЕ ПНЮ.

Answer 1

$Cos3 \alpha Cos \alpha = \frac{Cos(3 \alpha + \alpha )+Cos(3 \alpha - \alpha )}{2}= \frac{Cos4 \alpha+Cos2 \alpha }{2} \\\\\\Sin5 \alpha Sin3 \alpha = \frac{Cos(5 \alpha -3 \alpha )-Cos(5 \alpha +3 \alpha )}{2} = \frac{Cos2 \alpha -Cos8 \alpha }{2} \\\\\\Cos \alpha Cos2 \alpha= \frac{Cos( \alpha +2 \alpha )+Cos( \alpha -2 \alpha )}{2}= \frac{Cos3 \alpha +Cos \alpha }{2} \\\\\\ Sin2 \alpha Sin3 \alpha = \frac{Cos(2 \alpha -3 \alpha )-Cos(2 \alpha +3 \alpha )}{2} = \frac{Cos \alpha -Cos5 \alpha }{2}$