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Which one is not periodic

$\begin{array}{1 1}(a)\;\mid \sin 3x\mid+\sin^2x&(b)\;\cos\sqrt x+\cos^2x\\(c)\;\cos 4x+\tan^2x&(d)\;\cos 2x+\sin x\end{array}$

1 Answer

If a function $f$ is continuous and periodic on $R$, then it is uniformly continuous on $R$.
But the function $\cos \sqrt{x}$ is continuous but not uniformly continuous on $R$.
Hence it is not periodic
$\therefore \cos \sqrt{x} + \cos^2 x $ is not periodic
answered Oct 4, 2013 by sreemathi.v
edited Nov 6, 2017 by priyanka.c