AP EAMCET · Maths · Trigonometric Equations
If \(A=\left\{x \in[0,2 \pi] / \tan x-\tan ^2 x>0\right\}\) and \(B=\left\{x \in[0,2 \pi] /|\sin x| < \frac{1}{2}\right\}\), then \(A \cap B=\)
- A \(\left(0, \frac{\pi}{6}\right) \cup\left(\pi, \frac{7 \pi}{6}\right)\)
- B \(\left(0, \frac{\pi}{4}\right) \cup\left(\pi, \frac{7 \pi}{6}\right)\)
- C \(\left(0, \frac{\pi}{6}\right) \cup\left(\frac{5 \pi}{6}, \frac{7 \pi}{6}\right)\)
- D \(\left(\frac{\pi}{6}, \frac{7 \pi}{6}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(0, \frac{\pi}{6}\right) \cup\left(\pi, \frac{7 \pi}{6}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { If } A=\left\{x \in[0,2 \pi] / \tan x-\tan ^2 x>0\right\} \\ & \therefore \quad \tan x-\tan ^2 x>0 \\ & \Rightarrow \tan x(1-\tan x)>0 \\ & \quad 0 \frac{-1}{2} \\ & \Rightarrow \quad 0 < x < \frac{\pi}{6} \text { and }\left(\frac{5 \pi}{6}, 2…
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