According to the sources, when an AC voltage $V = V_m \sin(\omega t)$ is applied to a pure inductor, the resulting current lags the voltage by one-quarter cycle ($\pi/2$), which is expressed as $i = I_m \sin(\omega t - \pi/2) = -I_m \cos(\omega t)$ . The instantaneous power ($p_L$) supplied to the inductor is the product of the instantaneous voltage and current: $p_L = Vi = (V_m \sin \omega t)(-I_m \cos \omega t) = -V_m I_m \sin \omega t \cos \omega t$. By applying the trigonometric identity $\sin(2\omega t) = 2 \sin \omega t \cos \omega t$, the expression simplifies to $p_L = -\frac{V_m I_m}{2} \sin(2\omega t)$ .