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Graph of Trigonometric Ratios

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Question

The function $f (x) = sin \frac{π x}{2} + 2 cos \frac{π x}{3} - tan \frac{π x}{4}$ is periodic with period

A

3

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B

4

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C

12

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D

6

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Solution

The correct option is C $12$
Period of $sin \frac{π x}{2} = \frac{2 π}{π / 2} = 4$
Period of $cos \frac{π x}{3} = \frac{2 π}{π / 3} = 6$
Period of $tan \frac{π x}{4} = \frac{π}{π / 4} = 4$

$∴$ Period of $f (x) = L . C . M (4, 6, 4) = 12$

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