учтём, что 1 = log₄4 и пропотенцируем.
1) Ctg²(x -1) = 4Cos²(x-1)
2) Ctg²(x -1) - 4Cos²(x-1) = 0
3) Cos²(x -1)/ Sin²(x -1) -4Cos²(x -1) = 0
4) Cos²(x -1) - 4Cos²(x -1) Sin²(x -1) = 0, Cos²(x -1) (1 - 4Sin²(x -1)) = 0
Sin²(x -1) ≠ 0, ⇒ x -1 ≠ π/2 + πk , k ∈Z,
5) Cos²(x -1) = 0 или (1 - 4Sin²(x -1)) = 0
x ≠ 1 + π/2 + πk , k ∈Z,
6) x -1 = π/2 + πn , n ∈Z Sin²(x -1) = 1/4
x ≠ 1 + π/2 + πk , k ∈Z,
7) Sin(x -1) = +- 1/2, ⇒ х -1 = (-1)ⁿ *(+-π/6) + πn , n ∈Z
x ≠ 1 + π/2 + πk , k ∈Z
8) Ответ: х = 1 +-π/6 + πn , n ∈Z