(cos 23pi/12-sin 11pi/12)*(sin 17pi/12-cos19pi/12)

(cos23π/12-sin11π/12)(sin17π/12-cos19π/12)=(cos(2π-π/12)-sin(π-π/12))*(sin(π+5π/12)-cos(2π-5π/12)=(cosπ/12-sinπ/12)(-sin5π/12-cos5π/12)=(cosπ/12-sinπ/12)(-sin(π/2-π/12)-cos(π/2-π/12))==(cosπ/12-sinπ/12)(-1)(cosπ/12+sinπ/12)=-(cos²π/12-sin²π/12)=-cosπ/6=-√3/2