Sin(73П/24)*sin(37П/24)*sin(37П/12). Вычислить.

Question

Sin(73П/24)*sin(37П/24)*sin(37П/12). Вычислить.

Answer 1

Sin(73π/24)*sin(37π/24)*sin(37π/12)=sin(3π+π/24)sin(π+13π/24)sin(3π+π/12)=
-sinπ/24*(-sin13π/24)*(-sinπ/12)=-1/2(cos(13π/24-π/24)-cos(13π/24+π/24))*
*sinπ/12=-1/2(cosπ/2-cos7π/12)*sinπ/12=1/2cos7π/12*sinπ/12=
=1/4(sin(π/12-7π/12)+sin(π/12+7π/12))=1/4(sin(-π/2)+sin2π/3)=
=1/4*(-1)+1/4*√3/2=-1/4+√3/8