Решение
tg(2x) - tg(5х) = 0
sin(2x - 5x) / [cos(2x) * cos(5x)] = 0
1) sin(-3x) = 0
- 3x = πn, n∈Z
x = - πn/3, n ∈ Z
2) cos2x * cos(5x) ≠ 0
cos(2x) ≠ 0
2x ≠ π/2 + πk, k ∈ Z
x ≠ π/4 + πk/2, k ∈ Z
cos(5x) ≠ 0
5x ≠ π/2 + πm, m ∈ Z
x ≠ π/10 + πm/5, m ∈ Z
Ответ: x = - πn/3, n ∈ Z