Question

2sin^2x-cos x-1=0
Решить уравнение
Помогите какие будут корни.. -1/2 и 1 или 1/2 и -1.

Answer 1

2 sin²x - cos x - 1 = 0
2(1 - cos²x) - cos x -1 = 0
2 - 2 cos²x - cos x - 1 = 0
- 2 cos²x - cos x + 1 = 0
2 cos²x + cos x - 1 = 0
D = 1 + 8 = 9
√D = 3
cosx₁ = (-1 - 3): 4 = -1
cosx₂ = (-1 + 3): 4 = 1/2
x₁= π + 2πn
x₂ = π/3 + 2πn
x₃ = -π/3 + 2πn