Tg²x - 5 = 4 tg x
Через дискриминант.​

Tg²x - 5 = 4tgx tg²x - 4tgx - 5 = 0 Пусть tgx = a a² - 4a - 5 = 0 D = (-4)² - 4*(-5) = 16 + 20 = 36 a₁ = (4 + √36)/2 = (4 + 6)/2 = 5 a₂ = (4 - √36)/2 = (4 - 6)/2 = - 1 tgx₁ = 5 tgx₂ = - 1 x₁ = arctg5 + πn, n ∈ z x₂ = arctg(- 1) + πn, n ∈ z x₂ = - π/4 + πn, n ∈ z