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 $