The period of sin πx12+cos πx4+tanπx3,Where x represents the greatest integer less than or equal x is

Solution:

Since,
$\sin \frac{π [x + 24]}{12} = \sin \frac{π}{12} (24 + [x]) = \sin (2 π + \frac{π [x]}{2}) = \sin \frac{π [x]}{12}$
The period of $\sin \frac{π [x]}{12} is 24 .$
Similarly, period of $\cos \frac{π [x]}{4}$ is 8 and period of $\tan \frac{π [x]}{3} = 3$ .
Hence, the period of the given function $= LCM of 24, 8, 3 = 24 .$

The period of $\sin \frac{π [x]}{12} + \cos \frac{π [x]}{4} + \tan \frac{π [x]}{3},$ Where $[x]$ represents the greatest integer less than or equal x is

Solution:

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