Question

Решите неравенство $4cos^{2} x-3\geq 0$

A) (-3; 0) U [2; 4]
B) [-3; 0] U (2; 4)
C) (-∞; -3) U (0; 2) U (4; ∞)
D) (-3; 0] U [2; 4)

Answer 1

4cos²x-3≥0
cos²x≥3/4
|cosx|≥√3/2
[cosx≥√3/2
[cosx≤-√3/2
1)cosx≥√3/2
-π/6+2πk≤x≤π/6+2πk
2)cosx≤-√3/2
5π/6+2πk≤x≤4π/3+2πk