17. ctg² (2t – π/3) = 3

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

Решаем уравнение ctg²(2t - π/3) = 3:

Берем квадратный корень из обеих частей: ctg(2t - π/3) = ±√3

2t - π/3 = π/6 + πn, 2t - π/3 = -π/6 + πn

2t = π/6 + π/3 + πn, 2t = -π/6 + π/3 + πn

2t = π/2 + πn, 2t = π/6 + πn

t = π/4 + πn/2, t = π/12 + πn/2

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