Пошаговое объяснение:
Домножим числитель и знаменатель на 8sin(2π/7)*sin(3π/7)*sin(6π/7); воспользуемся формулой 2sin(α)*сosα=sin(α) и формулами приведения, получим
(2sin(2π/7)*сos(2π/7))*(2sin(3π/7)*сos2(3π/7))*
(2sin(6π/7)сos2(6π/7))/( 8sin(2π/7)*sin(3π/7)*sin(6π/7)=
sin(4π/7)*sin(6π/7)*sin(12π/7)/( 8sin(2π/7)*sin(3π/7)*sin(6π/7)=
sin(4π/7)*sin(12π/7)/( 8sin(2π/7)*sin(3π/7))=
sin(π-3π/7)*sin(2π-2π/7)/( 8sin(2π/7)*sin(3π/7))=
sin(3π/7)*sin(-2π/7)/( 8sin(2π/7)*sin(3π/7))=-1/8
Пошаговое объяснение:
Домножим числитель и знаменатель на 8sin(2π/7)*sin(3π/7)*sin(6π/7); воспользуемся формулой 2sin(α)*сosα=sin(α) и формулами приведения, получим
(2sin(2π/7)*сos(2π/7))*(2sin(3π/7)*сos2(3π/7))*
(2sin(6π/7)сos2(6π/7))/( 8sin(2π/7)*sin(3π/7)*sin(6π/7)=
sin(4π/7)*sin(6π/7)*sin(12π/7)/( 8sin(2π/7)*sin(3π/7)*sin(6π/7)=
sin(4π/7)*sin(12π/7)/( 8sin(2π/7)*sin(3π/7))=
sin(π-3π/7)*sin(2π-2π/7)/( 8sin(2π/7)*sin(3π/7))=
sin(3π/7)*sin(-2π/7)/( 8sin(2π/7)*sin(3π/7))=-1/8