WBJEE · Maths · Trigonometric Equations
\(\{x \in R: |\cos x | \geq \sin x\} \cap\left[0, \frac{3 \pi}{2}\right]\) is equal to
- A \(\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4}, \frac{3 \pi}{2}\right]\)
- B \(\left[0, \frac{\pi}{4}\right] \cup\left[\frac{\pi}{2} \cdot \frac{3 \pi}{2}\right]\)
- C \(\left[0, \frac{\pi}{4}\right] \cup\left[\frac{5 \pi}{4} \cdot \frac{3 \pi}{2}\right]\)
- D \(\left[0, \frac{3 \pi}{2}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4}, \frac{3 \pi}{2}\right]\)
Step-by-step Solution
Detailed explanation
Given, \(\{x \in R:|\cos x| \geq \sin x\} \cap\left[0, \frac{3 \pi}{2}\right]\) If we draw the graphs of \(|\cos x|\) and \(\sin x,\) clearly \(|\cos x| \geq \sin x\) when \(x \in\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4} \cdot \frac{3 \pi}{2}\right]\)…
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