The following code snippet will guide you through the issue chronologically.
\documentclass[preview,border=12pt,12pt]{standalone}
\usepackage{mathtools}
\begin{document}
\section*{gather+aligned}
\begin{gather}
\left\{\!
\begin{aligned}
x &= \cos t\\
y &= \sin t
\end{aligned}\right.\\
x^2 +y^2 =1
\end{gather}
\section*{gather+split}
\begin{gather}
\left\{
\begin{split}
x &= \cos t\\
y &= \sin t
\end{split}\right.\\
x^2 +y^2 =1
\end{gather}
\section*{align+aligned}
\begin{align}
&\left\{\!
\begin{aligned}
x &= \cos t\\
y &= \sin t
\end{aligned}\right.\\
&x^2 +y^2 =1
\end{align}
\section*{align+split}
It cannot be compiled.
%\begin{align}
%&\left\{
%\begin{split}
%x &= \cos t\\
%y &= \sin t
%\end{split}\right.\\
%&x^2 +y^2 =1
%\end{align}
\section*{align+split+nobrace}
It can be compiled.
\begin{align}
&
\begin{split}
x &= \cos t\\
y &= \sin t
\end{split}\\
&x^2 +y^2 =1
\end{align}
\end{document}

Why can't split with curly-brace \left\{ and \right. be inside align but it can be inside gather?
\left\{to the left and\right.to the right of thesplitmaterial." but apparently it works insidegatheras shown in my code given above. – kiss my armpit Jul 18 '14 at 08:05gatherexample you've given -- one can indeed getsplitto work. However, it might not work in other circumstances. So either the user guide is a bit too strident, or it's actually trying to give helpful advice by steering you away from trouble without covering every single possible contingency and circumstance. The upshot, though, is correct: Don't usesplitinsidegatherandalignenvironments. Usealignedinstead, unless you want to run into problems from time to time... – Mico Jul 18 '14 at 08:30casesconstructions – daleif Jul 18 '14 at 08:34splitis only recommended forequation? – kiss my armpit Jul 18 '14 at 13:07splitwhenever its material will be the only material on a given line. – Mico Jul 18 '14 at 13:11