Sin(pi/18)cos(pi/9)cos(2pi/9)

Question

Sin(pi/18)cos(pi/9)cos(2pi/9)

Answer 1

Решение смотрите на картинке

Answer 2

Домножим и разделим на cos(π/18)
(sinπ/18*cosπ/18*cosπ/9*cos2π/9)/cosπ/18=
=(sinπ/9*cosπ/9*cos2π/9)/(2cosπ/18)=
=(sin2π/9*cos2π/9)/(4cosπ/18)=
=(sin4π/9)/(8cosπ/18)=
=sin(π/2-π/18)/(8cosπ/18)=
=(cosπ/18)/(8cos(π/18)=
=1/8