(2Sin^2(Π/4)-Sin^2A)/Sin((Π/3)+A)*Sin((Π/3)-A)+Sin((Π/6)+A)*Cos((Π/3)+A)

Числитель: 2 * (1 - Cos(2 * Π/4))/2 - Sin^2A = 1 - Cos(2 * Π/4) - Sin^2A = 1 - 0 - Sin^2A;

Знаменатель: (Sin(Π/3) * CosА + Cos(Π/3) * SinА) * (Sin(Π/3) * CosА - Cos(Π/3) * SinА) + (Sin(Π/6) * CosА + Cos(Π/6) * SinА) * (Cos(Π/3) * CosА - Sin(Π/3) * SinА) = (√3/2 * CosА + 1/2 * SinА) * (√3/2 * CosА - 1/2 * SinА) + (1/2 * CosА + √3/2 * SinА) * (1/2 * CosА - √3/2 * SinА)= (√3/2 * CosА)^2 - (1/2 * SinА)^2 + (1/2 * CosА)^2 - (√3/2 * SinА)^2 = (3 + 3* Cos2А - 1 + Cos2А - 1 - Cos2А + 3 - 3 * Cos2А)/8 = 4/8;

Ответ: (1 - Sin^2A) * 8/4 = 2 - 2 * Sin^2A.