Sinx+cosx*ctgx/2 = - корень из 3

sinx + cosx * ctg(x/2) = -sqrt(3);sinx + cosx * cos(x/2)/sin(x/2) = -sqrt(3);(sinx * sin(x/2)) + cosx * cos(x/2) = -sqrt(3) * sin(x/2);1/2(cos (x - x/2) - cos(x + x/2)) + 1/2(cos(x + x/2) + cos(x - x/2)) = -sqrt(3) * sin(x/2);1/2cos(x/2) - 1/2cos(3x/2) + 1/2cos(3x/2) + 1/2cos(x/2) = -sqrt(3) * sin(x/2);cos(x/2) = -sqrt(3) * sin(x/2);cos(x/2) + sqrt(3) * sin(x/2) = 0;2 * (1/2 * cos(x/2) + sqrt(3)/2 * sin(x/2)) = 0;2 * sin(pi/6 + (x/2)) = 0;pi/6 + (x/2) = pin, n ∈ Z;x/2 = -pi/6 + pin, n ∈ Z;x = -pi/3 + 2pin, n ∈ Z.Ответ: -pi/3 + 2pin, n ∈ Z.Пояснение: Используем формулы произведения синусов и произведения косинусов.