Q. Solution of the inequality tan $\left( x + \frac{\pi}{3} \right) \geq 1\$is
A) $\left( n\pi + \frac{\pi}{12},n\pi + \frac{\pi}{6} \right)$
B) $\left( n\pi - \frac{\pi}{12},n\pi + \frac{\pi}{6} \right)$
C) $\left( n\pi - \frac{\pi}{6},n\pi - \frac{\pi}{12} \right)$
D) None of these
Explanation
(b)
$\because\tan{\left( x + \frac{\pi}{3} \right) \geq 1 \Rightarrow \frac{\pi}{4} \leq x + \frac{\pi}{3} < \frac{\pi}{2}}$
$\Rightarrow - \frac{\pi}{12} \leq x < \frac{\pi}{6}$
$\Rightarrow n\pi - \frac{\pi}{12} \leq x \leq n\pi + \frac{\pi}{6}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.