8.1 Trigonometric relations
$$
\begin{align} \sin 2\phi = 2\sin\phi\cos\phi, & \qquad \cos 2\phi =
\cos^2\phi - \sin^2\phi
\tag{8.1}\\ \cos^2\phi = \frac{1}{2} \left (1 + \cos 2
\phi \right ), & \qquad \sin^{2} \phi= \frac{1}{2} \left (1 - \cos 2
\phi \right) \tag{8.2}
\end{align}
$$