\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
f (z)
 & = & \sec z \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
f (z)
 & = & \sec z \\
& = & \frac{1}{\cos z} \\
& = & \frac{1}{\cos (x + iy)} \\
& = & \frac{1}{\cos x \cos (iy) - \sin x \sin (iy)} \\
& = & \frac{1}{\cos x \cosh y - i \sin x \sinh y} \\
& = & \frac{1}{\cos x \cosh y - i \sin x \sinh y} \frac{\cos x \cosh y + i \sin x \sinh y}{\cos x \cosh y + i \sin x \sinh y} \\
& = & \frac{\cos x \cosh y + i \sin x \sinh y}{(\cos x \cosh y)^{2} + (\sin x \sinh y)^{2}} \\
& = & \underbrace{\frac{\cos x \cosh y}{(\cos x \cosh y)^{2} + (\sin x \sinh y)^{2}}}_{u}
 + i \underbrace{\frac{\sin x \sinh y}{(\cos x \cosh y)^{2} + (\sin x \sinh y)^{2}}}_{v} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\frac{\partial u}{\partial x} - \frac{\partial v}{\partial y}
 & = & 0 \quad \wedge \quad \frac{\partial v}{\partial x} + \frac{\partial u}{\partial y} \, \, \, = \, \, \, 0 \\
\end{eqnarray*}
\end{document}
