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

Решение2ctg(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 = 0tg(x-1) = t3t² - 5t + 2 = 0D = 25 - 4*3*2 = 1t₁ = (5 - 1)/6t₁ = 2/3t₂ = (5 + 1)/6t₂ = 11)  tg(x-1) = 2/3x - 1 = arctg(2/3) + πk, k ∈ Z x₁ = arctg(2/3) + 1 + πk, k ∈ Z 2) tg(x-1) = 1x-1 = π/4 + πn, n ∈ Zx₂ = π/4 + 1 + πn, n ∈ ZОтвет: x₁ = arctg(2/3) + 1 + πk, k ∈ Z ; x₂ = π/4 + 1 + πn, n ∈ Z