4+5cosx-2sin²x=0
4 +5Cosx - 2(1 - Cos²x) = 0
4 +5Cosx -2 + 2Cos²x = 0
2Cos²x + 5Cosx +2 = 0
Cosx = y
2y² + 5y + 2 = 0
D = 9
y = (-5 +3)/4= -1/2
у= (-5 -3)/4 = -2
а) Cosx = -1/2
x = +-arcCos(-1/2) + 2πk , k ∈ Z
x = +-2π/3 + 2πk , k ∈ Z
б)Cosx = -2
∅
Ответ: x = +-2π/3 + 2πk , k ∈ Z