The function f(x) = ( ‎x 2 ) + ( ‎x 2 ) is periodic with period: - Vidyadip

MCQ

The function $ \text{f}(\text{x}) = \sin \Big(\frac{\pi‎\text{x}}{2}\Big) +\cos \Big(\frac{\pi‎\text{x}}{2}\Big)$ is periodic with period:

✓
4
B
6
C
12
D
24

✓

Answer

Correct option: A.

4

Period of $\sin \Big(\frac{\pi‎\text{x}}{2}\Big) = 2\pi\Big(\frac{\pi}{2}\Big) = 4$
Period of $\cos \Big(\frac{\pi‎\text{x}}{2}\Big) = 2\pi\Big(\frac{\pi}{2}\Big) = 4$
So, period of f(x) = LCM (4, 4) = 4

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