how to add explicit equation number in aligned environment?

Question

I have looked at all related questions and not able to find solution. I have to use aligned and since aligned does not support tag, how would one add an explicit equation number?

Here is MWE

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{adjustbox}

\begin{document}
\begin{equation*} 
\adjustbox{max width=\textwidth}{%
$
\begin{aligned}
x &= y \sin(x)  \\
  &= \cos(x)    %How to number this line? \tag{3} does not work
\end{aligned}
$}
\end{equation*}
\end{document}

I do not want an automatic equation number on the equation itself. But I want to add a specific equation number on one of the equations inside aligned itself.

I tried to do it by hand, but I do not know the amount of hspace to add to make the equation number show up at the right edge of the page as what happens automatically when using tag

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{adjustbox}

\begin{document}    
\begin{equation*} 
\adjustbox{max width=\textwidth}{%
$
\begin{aligned}
x &= y \sin(x)  \\
  &= \cos(x)   \hspace*{20pt} \text{(3)}  %how to know how much space?
\end{aligned}
$}
\end{equation*}
\end{document}

Thanks for any suggestions how to do the above.

Answer 1

Too big for a comment ...

Forcing tag to text border nullifies the effect of \adjustbox. For example, compare the following examples:

Both give the very same result.

\documentclass[12pt]{article}
\usepackage{amsmath,tabularx,adjustbox}
%% Automatic math-mode versions of l, r, and c column types:
\newcolumntype{L}{>{$\displaystyle}l<{$}}  
\newcolumntype{R}{>{$\displaystyle}r<{$}}
\newcolumntype{C}{>{$\displaystyle{}}c<{{}$}}

\begin{document}
\[
\setlength\tabcolsep{0pt} % <-- important
\adjustbox{max width=\textwidth}{%
  \begin{tabularx}{\linewidth}{X RCL >{\raggedleft\arraybackslash}X}
      & x & = & y \sin(x)  &     \\
      &   & = &   \cos(x)  & (3)  
  \end{tabularx}% <-- this comment symbol is needed
  }
\]

\begin{align}
    x & = y \sin(x) \notag  \\
      & =   \cos(x) \tag{3}
\end{align}    
\end{document}