17. ctg² (2t-π/3)=3

Ответ: t = π/3 + πn/2, n ∈ Z или t = π/6 + πn/2, n ∈ Z

• ctg² (2t - π/3) = 3
• ctg (2t - π/3) = ±√3

Решаем уравнение ctg (2t - π/3) = √3:

• 2t - π/3 = arcctg(√3) + πn, n ∈ Z
• 2t - π/3 = π/6 + πn, n ∈ Z
• 2t = π/6 + π/3 + πn, n ∈ Z
• 2t = π/2 + πn, n ∈ Z
• t = π/4 + πn/2, n ∈ Z

Решаем уравнение ctg (2t - π/3) = -√3:

• 2t - π/3 = arcctg(-√3) + πn, n ∈ Z
• 2t - π/3 = 5π/6 + πn, n ∈ Z
• 2t = 5π/6 + π/3 + πn, n ∈ Z
• 2t = 7π/6 + πn, n ∈ Z
• t = 7π/12 + πn/2, n ∈ Z

Ответ: t = π/4 + πn/2, n ∈ Z или t = 7π/12 + πn/2, n ∈ Z