Решите уравнение tgx-4ctgx=3

Tgx-4ctgx=3

ОДЗ: х≠ (πk) / 2, k-Z

tgx-4/tgx-3=0 |•tgx

tg²x-3tgx-4=0, Замена:tgx=t

t²-3t-4=0

D=9+16=25=5²

t1 = (3+5) / 2=4

t2 = (3-5) / 2=-1

tgx=-1; x1=-π/4+πn, n-Z

tgx=4; x2=arctg4+πm, m-Z