Решение
Tg(2x- п/4) +ctg(2x- п/4)=-2
tg(2x - π/4) + 1/tg(2x - π/4) + 2 = 0 умножим на tg(2x - π/4)
tg² (2x - π/4) + 2tg(2x - π/4) + 1 = 0
Пусть tg(2x - π/4) = z
z² + 2z + 1 = 0
(z + 1)² = 0
z = - 1
tg(2x - π/4) = - 1
2x - π/4 = - π/4 + πk, k∈Z
2x = π/4 - π/4 + πk, k∈Z
2x = πk, k∈Z
x = πk/2, k∈Z