Question

Period of $cos\frac{\pi x}{4}-2cosec\frac{\pi x}{6}+5tan\frac{\pi x}{3}$ is

• A. $12$
• B. $24$
• C. $48$
• D. $6$

Answer 1

Answer: (B)

$24$

Given $\cos \frac{\pi x}{4}-2cosec\frac{\pi x}{6}+5\tan \frac{\pi x}{3}$
Fundamental period of $\cos ax$ is $\frac{2\pi }{a}$
So, period of $\cos \frac{\pi x}{4}$ is 8
Fundamental period of $cosecax$ is $\frac{2\pi }{a}$
So, period of $cosec\frac{\pi x}{6}$ is 12.
Fundamental period of $\tan ax$ is $\frac{\pi }{a}$
So, period of $\tan \frac{\pi x}{3}$ is 3
Now, period of given function $=$ LCM of $8,12,3=24$