NTA Abhyas JEE Main2020MathematicsTrigonometric EquationsPractice
The solution set of x ∈ - π , π for the inequality sin 2 x + 1 ≤ cos x + 2 sin x is
Options
- Ax ∈ 0 , π 6
- Bx ∈ π 6 , 5 π 6 ∪ 0
- Cx ∈ - π 6 , 5 π 6
- Dx ∈ - π 2 , π 2
Correct answer
B. x ∈ π 6 , 5 π 6 ∪ 0
Step-by-step solution
2 sin ⁡ x cos ⁡ x + 1 - cos ⁡ x - 2 sin ⁡ x ≤ 0 2 sin ⁡ x - 1 cos ⁡ x - 1 ≤ 0 Case I: cos ⁡ x = 1 ⇒ x = 0 Case II: otherwise cos ⁡ x < 1 ⇒ 2 sin ⁡ x - 1 ≥ 0 ⇒ sin ⁡ x ≥ 1 2 ⇒ x ∈ π 6 , 5 π 6 Hence, from case I and case II, x ∈ π 6 , 5 π 6 ∪ 0