A function out of the following whose
period is not $\pi$ is

$y={\sin }^{2}x=\frac{1}{2}[1-\cos 2x]$ Since period of $\cos x\text{ is }2\pi$ so period of $\cos 2x\text{ is }\pi \text{. }$

$y=1+{\cos }^{2}x=1+\frac{1}{2}(1+\cos 2x)$ The period of this is 

again $\pi$ The period of tan $x$is p so period of tan$(2p + 3)$ is
$\pi /2.$ If $f\left(x\right) = |\sin x|$then$f(x + p) = |\sin (x + p\left)\right| = |–\sin x| =$
$\sin x Á = f\left(x\right).$Thus the period of $f$is $\pi$