\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
f (x)
 & = & \tan^{n} (ax) \\
& = & \frac{1}{\cot^{n} (ax)} \\
& = & \cot^{-n} (ax) \\
n
 & = & \mbox{oneven} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\cos^{2} \alpha + \sin^{2} \alpha
 & = & 1 \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \int \tan^{n} (ax) \, \mbox{d}x \\
& = & \int \frac{\sin^{n} (ax)}{\cos^{n} (ax)} \, \mbox{d}x \\
& = & \int \frac{\sin (ax) \sin^{n - 1} (ax)}{\cos^{n} (ax)} \, \mbox{d}x \\
& = & \int \frac{\sin (ax) (\sin^{2} (ax))^{(n - 1)/2}}{\cos^{n} (ax)} \, \mbox{d}x \\
& = & \int \frac{\sin (ax)}{\cos^{n} (ax)} (1 - \cos^{2} (ax))^{(n - 1)/2} \, \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 \frac{\sin (ax)}{\cos^{n} (ax)} (1 - \cos^{2} (ax))^{(n - 1)/2} \, \mbox{d}x \\
& = & \int \frac{\sin (ax)}{\cos^{n} (ax)}
 \sum_{i = 0}^{i = (n - 1)/2} \left ( {(n - 1)/2 \atop i} \right ) 1^{(n - 1)/2 - i} (- \cos^{2} (ax))^{i} \, \mbox{d}x \\
& = & \int \frac{\sin (ax)}{\cos^{n} (ax)}
 \sum_{i = 0}^{i = (n - 1)/2} \left ( {(n - 1)/2 \atop i} \right ) (-1)^{i} \cos^{2i} (ax) \, \mbox{d}x \\
& = & \int \frac{\sin (ax)}{\cos^{n} (ax)}
 \Biggl ( \sum_{i = 0}^{i = (n - 1)/2 - 1} \left ( {(n - 1)/2 \atop i} \right ) (-1)^{i} \cos^{2i} (ax) \\
 & & \qquad \qquad \qquad + \, \left ( {(n - 1)/2 \atop (n - 1)/2} \right ) (-1)^{(n - 1)/2} \cos^{2 (n - 1)/2} (ax) \Biggr ) \, \mbox{d}x \\
& = & \int \frac{\sin (ax)}{\cos^{n} (ax)}
 \left ( \sum_{i = 0}^{i = (n - 1)/2 - 1} \left ( {(n - 1)/2 \atop i} \right ) (-1)^{i} \cos^{2i} (ax)
 + (-1)^{(n - 1)/2} \cos^{n - 1} (ax) \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \int
 \left ( \sum_{i = 0}^{i = (n - 3)/2} \left ( {(n - 1)/2 \atop i} \right ) (-1)^{i} \cos^{2i - n} (ax)
 + (-1)^{(n - 1)/2} \cos^{n - 1 - n} (ax) \right ) \, \mbox{d}(\cos (ax)) \\
& = & - \frac{1}{a} \int
 \left ( \sum_{i = 0}^{i = (n - 3)/2} \left ( {(n - 1)/2 \atop i} \right ) (-1)^{i} \cos^{2i - n} (ax)
 + (-1)^{(n - 1)/2} \cos^{-1} (ax) \right ) \, \mbox{d}(\cos (ax)) \\
& = & - \frac{1}{a}
 \left ( \sum_{i = 0}^{i = (n - 3)/2} \left ( {(n - 1)/2 \atop i} \right ) \frac{(-1)^{i}}{2i - n + 1} \cos^{2i - n + 1} (ax)
 + (-1)^{(n - 1)/2} \ln \cos (ax) \right ) \\
& = & \frac{1}{a}
 \left ( \sum_{i = 0}^{i = (n - 3)/2} \left ( {(n - 1)/2 \atop i} \right ) \frac{(-1)^{i}}{n - 2i - 1} \sec^{n - 2i - 1} (ax)
 + (-1)^{(n + 1)/2} \ln \cos (ax) \right ) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \frac{1}{a} \left ( \sum_{i = 0}^{i = (n - 3)/2} \left ( {(n - 1)/2 \atop i} \right ) \frac{(-1)^{i}}{n - 2i - 1} \sec^{n - 2i - 1} (ax)
 + (-1)^{(n + 1)/2} \ln | \, \cos (ax) \, | \right ) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \frac{1}{a} \Biggl ( (-1)^{(n + 1)/2} \ln | \, \cos (ax) \, | \\
 & & \qquad + \, \sum_{i = 0}^{i = (n - 3)/2} \left ( {(n - 1)/2 \atop i} \right ) \frac{(-1)^{i}}{n - 2i - 1} \sec^{n - 2i - 1} (ax) \Biggr ) \\
\end{eqnarray*}
\end{document}
