Functions Part 1

$\sqrt{x}$ is non periodic function and $\cos$ (something) is a periodic function so here in $\cos \sqrt{x} \rightarrow$ inside periodic function there is non periodic function which always produce non periodic function. $\cos^2 x$ is a periodic function with period $\pi$ Note: (1) When $n$ is odd then the period of $\sin^n \theta, \cos^n \theta, \csc^n \theta, \sec^n \theta = 2\pi$ (2) When $n$ is even then the period of $\sin^n \theta, \cos^n \theta, \csc^n \theta, \sec^n \theta = \pi$ (3) When $n$ is even/odd then the period of $\tan^n \theta, \cot^n \theta = \pi$ (3) When $n$ is even/odd then the period of $|\sin^n \theta|, |\cos^n \theta|, |\csc^n \theta|, |\sec^n \theta|, |\tan^n \theta|, |\cot^n \theta| = \pi$ $\cos \sqrt{x} + \cos^2 x =$ non periodic function $+$ periodic function $=$ non periodic function