Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.2 The Existence of the Laplace Transform and the Inverse Transform - True-False Review - Page 685: c

False

$\cos 2(t+\dfrac{\pi}{2})=\cos (2t+\pi) \\=\cos (2t) \cos (\pi)-\sin (2t) \sin (\pi) \\=-\cos (2t) -0\\=-\cos (2t)$ This implies that $\dfrac{\pi}{2}$ cannot be considered a period of function $\cos (2t)$. Therefore, the given statement is $\bf{False}$.