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$$\begin{align} p &= V(t)\ I(t) \\ p &= V_m \sin(\omega t) \ I_m \sin(\omega t + \phi) \\ p &= V_m I_m\ \sin(\omega t) \ \sin(\omega t + \phi) \\ \end{align}$$ Trigonometric identity: $$ \sin \alpha \ \sin \beta = \frac {\cos(\alpha - \beta) - \cos(\alpha + \beta)}{2} $$ $$\begin{align} p &= \frac {P_m} {2}\ [{ \cos(\omega t - \omega t - \...


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