Question

Решите,пожалуйста tg^2x-5=4tgx

Answer 1

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