The period of the function sin left( frac{pi | vedclass

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(A) The period of a function $f(x) = \sin(ax)$ is given by $T = \frac{2\pi}{|a|}$.For the term $\sin \left( \frac{\pi x}{2} \right)$,the period $T_1 =

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$4$

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(A) The period of a function $f(x) = \sin(ax)$ is given by $T = \frac{2\pi}{|a|}$.For the term $\sin \left( \frac{\pi x}{2} ight)$,the period $T_1 = \frac{2\pi}{\pi/2} = 4$.For the term $\cos \left( \frac{\pi x}{2} ight)$,the period $T_2 = \frac{2\pi}{\pi/2} = 4$.The period of the sum of two periodic functions is the least common multiple ($L$.$C$.$M$.) of their individual periods.Therefore,the period of $\sin \left( \frac{\pi x}{2} ight) + \cos \left( \frac{\pi x}{2} ight) = 	ext{L.C.M. of } (4, 4) = 4$.

The period of the function $\sin \left( \frac{\pi x}{2} \right) + \cos \left( \frac{\pi x}{2} \right)$ is

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