2ctg(x-1)+3tg(x-1)=5

Решение 2ctg(x-1)+3tg(x-1)=5  2*(1/tg(x-1)+3tg(x-1)=5 умножим на tg(x-1) ≠ 0  3tg²(x-1) - 5tg(x-1) + 2 = 0 tg(x-1) = t 3t² - 5t + 2 = 0 D = 25 - 4*3*2 = 1 t₁ = (5 - 1)/6 t₁ = 2/3 t₂ = (5 + 1)/6 t₂ = 1 1)  tg(x-1) = 2/3 x - 1 = arctg(2/3) + πk, k ∈ Z  x₁ = arctg(2/3) + 1 + πk, k ∈ Z  2) tg(x-1) = 1 x-1 = π/4 + πn, n ∈ Z x₂ = π/4 + 1 + πn, n ∈ Z Ответ: x₁ = arctg(2/3) + 1 + πk, k ∈ Z ; x₂ = π/4 + 1 + πn, n ∈ Z