Question

The period of $f\left(x\right)=\sin \frac{\pi x}{2}+2\cos \frac{\pi x}{3}-\tan \frac{\pi x}{4}$ is

• A. $6$
• B. $3$
• C. $4$
• D. $12$

Answer 1

The correct option is D $12$

Period of $\sin \frac{\pi x}{2}$ is $\frac{2\pi }{\pi /2}=4=T_1$

Period of $\cos \frac{\pi x}{3}$ is $\frac{2\pi }{\pi /3}=6=T_2$

Period of $\tan \frac{\pi x}{4}$ is $\frac{\pi }{\pi /4}=4=T_3$

Hence period of f is $=$ L.C.M. of $T_1,T_2,T_3$ $=12$