$\{x \in R: |\cos x | \geq \sin x\} \cap\left[0, \frac{3 \pi}{2}\right]$ is equal to

• Correct answer
  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

  $\left[0, \frac{3 \pi}{2}\right]$

Solution

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 $x \in\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4} \cdot \frac{3 \pi}{2}\right]$ $\therefore \quad x \in\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4}, \frac{3 \pi}{2}\right] \cap\left[0, \frac{3 \pi}{2}\right]$ $\Rightarrow \quad x \in\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4}, \frac{3 \pi}{2}\right]$

Hence, the correct answer is option: 'A'.