А вот другой вариант
cos2x + sin2x = 0
делим на cos2x ≠ 0 и получаем
1 + tg2x = 0
tg2x = -1
2x = -arctg (1) + πk
2x = -π/4 + πk
x = - π/8 + 0.5πk (k ∈ Z)
На промежутке
[2π; 4π]
2π ≤ -π/8 + 0.5πk ≤ 4π
17π/8 ≤ 0.5πk ≤ 4π
17π/4 ≤ πk ≤ 8π
17/4 ≤ k ≤ 8 → k = 5 , 6 , 7, 8
1) x1 = - π/8 + 2.5π → 19π/8
2) x2 = -π/8 +3π = 23π/8
3) x3 = - π/8 + 3.5π = 27π/8
4) x4 = -π/8 + 4π = 31π/8