Решение
1) 4tg²x-9=0
4tg²x = 9
tg²x = 9/4
a) tgx = -3/2
x1 = - arctg(3/2) + πn, n∈Z
tgx = 3/2
b) tgx = 3/2
x2 = arctg(3/2) + πk, k∈Z
Ответ: x1 = - arctg(3/2) + πn, n∈Z; x2 = arctg(3/2) + πk, k∈Z
2) 3tg²x-2tgx=0
tgx * (3tgx - 2) = 0
tgx = 0
x1 = πk, k∈Z
3tgx - 2 = 0
tgx = 2/3
x2 = arctg(3/2) + πn, n∈Z
Ответ: x1 = πk, k∈Z: x2 = arctg(3/2) + πn, n∈Z