Chapter 1, Problem 1.20P

Demonstrate that Equation (1-59) can be derived from Equation (1-58) using simple trigonometric identities. $\begin{array}{l}p\left(t\right)=v\left(t\right)i\left(t\right)=2VI\cos \omega t\cos \left(\omega t-\theta \right)\left(1-58\right)\\ p\left(t\right)=VI\cos \theta \left(1+\cos 2\omega t\right)+VI\sin \theta \sin 2\omega t\left(1-59\right)\end{array}$

Hint: The following identities will be useful: $\begin{array}{l}\cos \alpha \cos \beta =\frac{1}{2}\left[\cos \left(\alpha -\beta \right)+\cos \left(\alpha +\right)\right]\\ \cos \left(\alpha -\beta \right)=\cos \alpha \cos \beta +\sin \alpha \sin \beta \end{array}$