Решение
5sin²x - cosx + 1 = 0
5*(1 - cos²x) - cosx + 1 = 0
5 - 5cos²x - cosx + 1 = 0
5cos²x + cosx - 6 = 0
cosx = t, I t I ≤ 1
5t² + t - 6 = 0
D = 1 + 4*5*6 = 121
t₁ = (- 1 - 11)/10
t₁ = - 12/10
t₁ = 1,2 не удовлетворяет условию I t I ≤ 1
t₂ = (- 1 + 11)/10
t₂ = 1
cosx = 1
x = 2πk, k∈Z