\documentclass{article}
\pagestyle{empty}
\begin{document}
First equation:
$x^2 = y^2 + z^2$
Second equation:
\[
x = \frac{y}{z^2}
\]
Third equation:
\begin{equation}
\sin^2(x) + \cos^2(x)
\end{equation}
Fourth equation:
\begin{equation}
\tan^2(x) + \cos^2(x)
\end{equation}
\end{document}
