Cosx*tgx+cosx+tgx+1=0

Решение Cosx*tgx+cosx+tgx+1=0 Cosx*(sinx/cosx) + cosx + sinx/cosx + 1 = 0 умножим на сosx ≠ 0 sinx*cosx + cos²x + sinx + cosx = 0 cosx(sinx + cosx) + (sinx + cosx) = 0 (sinx + cosx)*(cosx + 1) = 0 1)  sinx + cosx = 0  делим на cosx ≠ 0 tgx + 1 = 0 tgx = 1 x₁ = π/4 + πk, k ∈Z 2)  cosx + 1 = 0 cosx = - 1 x₂ = π + 2πn, n∈Z Ответ: x₁ = π/4 + πk, k ∈Z ; x₂ = π + 2πn, n∈Z