An alternating emf of angular frequency $\omega$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency : 

The instantaneous values of emf and current in inductive circuit are given by

$[E={{E}_{0}}\sin \omega t]$ and $[i={{i}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right)]$ respectively.

So, $[{{P}_{inst}}=Ei={{E}_{0}}\sin \omega t\times {{i}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right)]$

$[={{E}_{0}}{{i}_{0}}\sin \omega t\left( \sin \omega t\cos \frac{\pi }{2}-\cos \omega t\sin \frac{\pi }{2} \right)]$

$[={{E}_{0}}{{i}_{0}}\sin \omega t\ \cos \omega t]$

$[=\frac{1}{2}{{E}_{0}}{{i}_{0}}\sin 2\omega t]$

$[(\sin 2\omega t=2\sin \omega t\ \cos \omega t)]$

Hence, angular frequency of instantaneous power is $[2\omega ].$