Question

Cosx*tgx+cosx+tgx+1=0

Answer 1

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