Q. The period of the function $f(x) = cosec^{2}3x + \cot{4x}$ is
A) $\frac{\pi}{3}$
B) $\frac{\pi}{4}$
C) $\frac{\pi}{6}$
D) $\pi$
Explanation
(d)
$f(x) = cosec^{2}3x + \cot{4x}$
Period of $cosec^{2}3x$ is $\frac{\pi}{3}$ and $\cot{4x}$ is $\frac{\pi}{4}$.
$\therefore$ Period of $f(x) =$ LCM of $\left\{ \frac{\pi}{3}\ and\ \frac{\pi}{4} \right\}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{LCM\ of\ (\pi,\ \pi)}{HCF\ of\ (3,\ 4)} = \frac{\pi}{1} = \pi$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.