Помогите решить уравнение 5tg x - 12ctg x + 11 = 0

5tgx - 12/tgx + 11 = 0

5tg²x + 11tgx - 12 = 0 (tgx ≠ 0)

Пусть t = tgx.

5t² + 11t - 12 = 0

D = 121 + 5•12•4 = 361 = 19²

t1 = (-11 + 19) / 10 = 8/10 = 4/5

t2 = (-11 - 19) / 10 = - 30/10 = - 3

Обратная замена:

tgx = 4/5

x = arctg (4/5) + πn, n ∈ Z

tgx = - 3

x = arctg (-3) + πn, n ∈ Z.