You can do with mathtools, but I wouldn't recommend it. This leaves a gap on the right of “sin”, but centering it in the available space would be even worse.
\documentclass{article}
\usepackage{mathtools}
\let\sin\relax % remove the previous definition of \sin
\DeclareMathOperator{\sin}{%
\mathrlap{\operatorname{sin}}\hphantom{\cos}%
}
\begin{document}
$\sin\alpha$
$\cos\alpha$
$e^{\sin x}$
$e^{\cos x}$
\end{document}

A different solution, where you add the space after the \sin<expression> can be
\documentclass{article}
\usepackage{mathtools}
\newcommand{\csin}[1]{%
\mathop{}\!\mathrlap{\sin#1}\hphantom{\cos#1}%
}
\begin{document}
$3\csin{\alpha}+\cos\beta$
$3\cos\alpha+\cos\beta$
$e^{\csin{x}+i\cos{x}}$
$e^{\cos x+i\cos x}$
\end{document}
Since we need to know what the argument to \csin is, braces delimiting it are necessary.
However, this has limitations because it's difficult to catch the type of the last object in the argument of \csin, so this might break with parenthesized expressions and hand corrections would be needed, for instance
\csin{(x+y)}\mathclose{}

Yet another proposal: a \sincorr space to be added by hand where necessary:
\documentclass{article}
\newcommand{\sincorr}{\mathpalette\dosincorr\relax}
\newcommand{\dosincorr}[2]{%
\sbox0{$#1\cos$}\sbox2{$#1\sin$}%
\kern\dimexpr\wd0-\wd2\relax}
\begin{document}
$3\sin\alpha\sincorr+\cos\beta$
$3\cos\alpha+\cos\beta$
$e^{\sin x\sincorr+i\cos x}$
$e^{\cos x+i\cos x}$
\end{document}
The output is identical as with the previous solution.
\mathop{\rlap{$\sin$}\hphantom{\cos}}instead of a negative phantom. – Hendrik Vogt Jun 25 '13 at 09:16Anyware I can read more about the usage of \rlap ?
– Fictional Jun 25 '13 at 09:22\rlapin tex by topic (texdoc texbytopicon a tex live system) in section 5.4.5, p.65. – barbara beeton Jun 25 '13 at 13:37\mathopso that before and after it you also get the same spacing as for\cos. – Hendrik Vogt Jun 30 '13 at 08:56