Time period $T =\frac{2 \pi}{\omega'}$
$\frac{\pi}{\omega}=\frac{2 \pi}{\omega'}$
$\omega'=2 \omega \rightarrow$ Angular frequency of SHM Option (3)
$\sin ^{2} \omega t =\frac{1}{2}\left(2 \sin ^{2} \omega t \right)=\frac{1}{2}(1-\cos 2 \omega t )$
Angular frequency of $\left(\frac{1}{2}-\frac{1}{2} \cos 2 \omega t\right)$ is $2 \omega$
Option (4)
Angular frequency of $SHM$
$3 \cos \left(\frac{\pi}{4}-2 \omega t\right)$ is $2 \omega$.
So option (3) & (4) both have angular frequency $2 \omega$ but option (4) is direct answer