\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
f (x)
 & = & \cos^{n} (ax) \\
& = & \frac{1}{\sec^{n} (ax)} \\
& = & \sec^{-n} (ax) \\
n
 & = & \mbox{oneven} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\sin^{2} \alpha + \cos^{2} \alpha
 & = & 1 \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \int \cos^{n} (ax) \, \mbox{d}x \\
& = & \int \cos (ax) \cos^{n - 1} (ax) \, \mbox{d}x \\
& = & \int \cos (ax) (\cos^{2} (ax))^{\frac{1}{2} (n - 1)} \, \mbox{d}x \\
& = & \int \cos (ax) (1 - \sin^{2} (ax))^{\frac{1}{2} (n - 1)} \, \mbox{d}x \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\left ( {u \atop v} \right )
 & = & \frac{u!}{v! (u - v)!} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
(p + q)^{s}
 & = & \left ( {s \atop 0} \right ) p^{s} + \left ( {s \atop 1} \right ) p^{s - 1} q + \left ( {s \atop 2} \right ) p^{s - 2} q^{2} + \ldots +
 \left ( {s \atop s - 2} \right ) p^{2} q^{s - 2} + \left ( {s \atop s - 1} \right ) p q^{s - 1} + \left ( {s \atop s} \right ) q^{s} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
(p + q)^{s}
 & = & \sum_{i = 0}^{i = s} \left ( {s \atop i} \right ) p^{s - i} q^{i} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \int \cos (ax) (1 - \sin^{2} (ax))^{\frac{1}{2} (n - 1)} \, \mbox{d}x \\
& = & \int \cos (ax)
 \sum_{i = 0}^{i = \frac{1}{2} (n - 1)} \left ( {\frac{1}{2} (n - 1) \atop i} \right ) 1^{\frac{1}{2} (n - 1) - i} (- \sin^{2} (ax))^{i} \, \mbox{d}x \\
& = & \int \cos (ax) \sum_{i = 0}^{i = \frac{1}{2} (n - 1)} \left ( {\frac{1}{2} (n - 1) \atop i} \right ) (-1)^{i} \sin^{2 i} (ax) \, \mbox{d}x \\
& = & \frac{1}{a} \int \sum_{i = 0}^{i = \frac{1}{2} (n - 1)} \left ( {\frac{1}{2} (n - 1) \atop i} \right ) (-1)^{i} \sin^{2 i} (ax) \, \mbox{d}(\sin (ax)) \\
& = & \frac{1}{a} \sum_{i = 0}^{i = \frac{1}{2} (n - 1)} \left ( {\frac{1}{2} (n - 1) \atop i} \right ) \frac{(-1)^{i}}{2 i + 1} \sin^{2 i + 1} (ax) + c \\
& = & \sum_{i = 0}^{i = \frac{1}{2} (n - 1)} \left ( {\frac{1}{2} (n - 1) \atop i} \right ) \frac{(-1)^{i}}{(2 i + 1) a} \sin^{2 i + 1} (ax) + c \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \sum_{i = 0}^{i = \frac{1}{2} (n - 1)} \left ( {\frac{1}{2} (n - 1) \atop i} \right ) \frac{(-1)^{i}}{(2 i + 1) a} \sin^{2 i + 1} (ax) + c \\
\end{eqnarray*}
\end{document}
