Find the period of the function f(x) = sin ((π x)/(2) ) + cos ((π x)/(3) ) — JEE Mathematics

• The period of $\sin(kx)$ is $\frac{2\pi}{|k|}$. Here, $k_1 = \frac{\pi}{2}$, so the period $T_1 = \frac{2\pi}{\pi/2} = 4$.
• The period of $\cos(kx)$ is $\frac{2\pi}{|k|}$. Here, $k_2 = \frac{\pi}{3}$, so the period $T_2 = \frac{2\pi}{\pi/3} = 6$.

The period of the combined function $f(x)$ is the Least Common Multiple (LCM) of $T_1$ and $T_2$:

$$T = LCM(4, 6) = 12$$

Answer: 12