Доказать: cos(pi/7)cos(4pi/7)cos(5pi/7)=1/8

Question

Доказать: cos(pi/7)cos(4pi/7)cos(5pi/7)=1/8

Answer 1

Cosπ/7*cos4π/7*(-cos2π/7)=(-sinπ/7*cosπ/7*cos2π/7*cos4π/7)/sinπ/7=
=(-sin2π/7*cosπ/7*cos2π/7*cos4π/7)/2sinπ/7=(-sin4π/7*cos4π/7)/4sinπ/7=
=(-sin8π/7)/8sinπ/7=(-sinπ/7)/8sinπ/7=-1/8