Question

The function $f(x)=sin\left(\frac{\pi x}{2}\right)+2cos\left(\frac{\pi x}{3}\right)-\tan \left(\frac{\pi x}{4}\right)$ is a periodic function. It's period is

• A. 6
• B. 3
• C. 4
• D. 12

Answer 1

Answer: (D)

Period of $\sin \frac{\pi x}{2}=\frac{2\pi }{\pi /2}=4$
Period of $\cos \frac{\pi x}{3}=\frac{2\pi }{\pi /3}=6$ and period of $\tan \frac{\pi x}{4}=\frac{\pi }{\pi /4}=4$
$\therefore$ Period of the given function
$f(x)$ = LCM of 4, 6 and 4 $=12$