Question

ПОМОГИТЕ СРОЧНО РЕШИТЬ


2in^2x-3 cosx+3=0

Answer 1

2Sin²x - 3Cosx + 3 = 0
2(1-Cos²x) - 3Cosx + 3 = 0
2 - 2Cos²x - 3Cosx + 3 = 0
-2Cos²x - 3Cosx + 5 = 0
2Cos²x + 3Cosx - 5 = 0
Cosx = t ∈ [-1;1]
2t² + 3t - 5 = 0
D = 9 - 4 * 2 * (-5) = 49
t₁ = (-3 + 7) / 4 = 1
t₂ = (-3 - 7) / 4 = -2.5 ∉ [-1;1]
Cosx = 1
x = 2πn, n∈Z