Question

сколько корней уравнения tg3x=1 принадлежит промежутку [0;пи]

Answer 1

tg3x=1
3x = π/4 + πn, n ∈ Z
x = π/12 + πn/3, n ∈ Z
при n = 0
x1 = π/12
при n = 1
x2 = π/12 + π/3 = (π + 4π)/12 = 5π/12
при n = 2
x3 = π/12 + 2π/3 = (π + 8π)/12 = 9π/12 = 3π/4
Ответ 3