МГ
Максим Гореликов
sin(2x) + 1 = sin(x) + 6ctg(x)
2sin(x)cos(x) + 1 = sin(x) + 6cos(x)/sin(x)
2sin(x)*cos(x) + cos(x) = 6cos(x)/sin(x)
cos(x)*(2sin(x) + cos(x) -6/sin(x)) = 0
cos(x) = 0
x = π/2 + πk, k - целое.
2sin(x) + cos(x) - 6/sin(x) = 0
2sin(x) + cos(x)sin(x) - 6 = 0
2tg(x) + tg(x) - 6 - 6tg(x) = 0
4tg(x) - tg(x) + 6 = 0 - нет решений.
Ответ: x = π/2 + πk, k - целое.