Statement (A): Period of $\cos^{3} x + \cos^{3} (120 ° - x) + \cos^{3} (120 ° + x)$ is $\frac{π}{3}$ .
Statement (B): Period of $2 \cos \frac{π x}{3} + \sin \frac{π x}{2} - \tan \frac{π x}{4}$ is 12.
Which of the above statements is correct?

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neither (A) nor (B)

both (A) and (B)

only (B)

only (A)

answer is D.

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Detailed Solution

Statement(I): Period of

\cos^{3} x (or) \cos^{3} (120 ° - x) (or) \cos^{3} (120 ° + x) = 2 π

$∴ L .C .M (2 π, 2 π, 2 π) = 2 π$

Statement(II): period of $\cos \frac{π x}{3} = \frac{2 π}{\frac{π}{3}} = 6$

Period of $\sin \frac{π x}{2} = \frac{2 π}{\frac{π}{2}} = 4$

Period of $\tan \frac{π x}{4} = \frac{π}{\frac{π}{4}} = 4$

$∴$ L.C.M of $(6, 4, 4) = 12$

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