AP EAMCET201825 Apr 2018Morning ShiftMathematicsTrigonometric EquationsActual
If A = x ∈ [ 0 , 2 π ] / tan x - tan 2 x > 0 and B = x ∈ [ 0 , 2 π ] / | sin x | < 1 2 , then A ∩ B =
Options
- A0 , π 6 ∪ π , 7 π 6
- B0 , π 4 ∪ π , 7 π 6
- C0 , π 6 ∪ 5 π 6 , 7 π 6
- Dπ 6 , 7 π 6
Correct answer
A. 0 , π 6 ∪ π , 7 π 6
Step-by-step solution
We have A = x ∈ [ 0 , 2 π ] / tan x - tan 2 x > 0 B = x ∈ [ 0 , 2 π ] / | sin x | < 1 2 For set A tan x - tan 2 x > 0 ⇒ tan x 1 - tan x > 0 ⇒ 0 < tan x < 1 From the graph, it is clear that for x ∈ 0 , π 4 ∪ π , 5 π 4 ⇒ tan x ∈ 0 , 1 , For set B | sin x | < 1 2 From the graph, it is clear that, for x ∈ 0 , π 6 ∪ 5 π 6 , 7 π 6 ∪ 11 π 6 , 2 π ⇒ sin x < 1 2 So, common