Explanation

(d) 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, $P_{inst} = Ei = E_{0}\sin{\omega t} \times i_{0}\sin\left( \omega t - \frac{\pi}{2} \right)$
$= E_{0}i_{0}\sin{\omega t}\left( \sin{\omega t}\cos{\frac{\pi}{2} - \cos{\omega t}\sin\frac{\pi}{2}} \right)$
$= E_{0}i_{0}\sin{\omega t}\cos{\omega t}$
$= \frac{1}{2}E_{0}i_{0}\sin{2\omega t}\ \ \ \left( \sin{2\omega t} = 2\sin{\omega t}\cos{\omega t} \right)$
Hence, angular frequency of instantaneous power is $2\omega$