\documentclass{article}
\usepackage{mathtools}
\usepackage{eqparbox}
\newcommand\eqmathbox[2][M]{\eqmakebox[M#1]{$\scriptstyle#2$}}
\newcommand{\prodsincos}{\prod_{j\in A}
\sin\alpha_j \prod_{j\notin A} \cos\alpha_j}
\begin{document}
\begin{align}
\begin{split} \label{fn of a+b}
\cos(\alpha+\beta) & = \cos\alpha\cos\beta - \sin\alpha\sin\beta \\
\sin(\alpha+\beta) & = \sin\alpha\cos\beta + \cos\alpha\sin\beta
\end{split}
\end{align}
\begin{alignat}{2}
\begin{split}
\cos \sum_j \alpha_j
& = \sum_{k=0}^\infty (-1)^k
&& \sum_{|A|=2k}
\prodsincos \\
\sin \sum_j \alpha_j
& = \sum_{k=0}^\infty (-1)^k
&&\sum_{|A|=2k+1}
\prodsincos
\end{split}
\end{alignat}
\end{document}
The code above works fine if I omit \begin{split} and \end{split}. The purpose of split was to get just one equation number. With split, I get this error message:
! Extra alignment tab has been changed to \cr.
<template> }$\hfill \endtemplate
What should I do?


equationshould be used for "one-line" (or one equation number) displays rather thatalignand friends. – barbara beeton Jun 06 '16 at 13:55