Question

cos(п/7)×cos(2п/7)×cos(3п/7)=?
(п-пи)
Решите и дайте объяснение пожалуйста

Answer 1

(sinπ/7*cosπ/7*cos2π/7*cos3π/7)/(sinπ/7)=
=(sin2π/7*cos2π/7*cos3π/7)/(2sinπ/7)=(sin4π/7*cos3π/7)/(4sinπ/7)=
=(sin(π-3π/7)*cos3π/7)/(4sinπ/7)=(sin3π/7*cos3π/7)/4sinπ/7)=
=(sin6π/7)/(8sinπ/7)=sin(π-π/7)/(8sinπ/7)=(sinπ/7)/(8sinπ/7)=1/8