The period of the function ( x 2 ) + ( x 2 ) is - Vidyadip

MCQ

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

✓
$4$
B
$6$
C
$12$
D
$24$

✓

Answer

Correct option: A.

$4$

a
(a) Period of $\sin \left( {\frac{{\pi x}}{2}} \right) = \frac{{2\pi }}{{\pi /2}} = 4$

Period of $\cos \,\left( {\frac{{\pi x}}{2}} \right) = \frac{{2\pi }}{{\pi /2}} = 4$

$\therefore $ Period of $\sin \frac{{\pi x}}{2} + \cos \frac{{\pi x}}{2} = $$L.C.M. of (4, 4)=4.$

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