How to skip latex error and generate document

Question

I am trying to generate image formula from latex (Formulas given by a third side). First of all i am writing a tex document, like:

\documentclass[12pt,border=5pt,varwidth]{standalone}
\usepackage{amsmath}
\usepackage[T1,T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[russian]{babel}
\usepackage[russian]{babel}
\DeclareMathSizes{12}{17.28}{12}{10}
\begin{document}
\begin{equation*}
\Leftrightarrow 
\left [ {
  \begin{align}
    &\sin x=\frac{\sqrt{3}}{2},\\
    &\cos x=1
  \end{align}
}\right. 
\Leftrightarrow
\left [ {
  \begin{align}
    &x=\frac{\pi}{3}+2\pi k, \\
    &x=\frac{2\pi}{3}+2\pi k, \\
    & x=2\pi k, k\in\mathbb{Z}.
  \end{align}
}\right.
\end{equation*}
\end{document}

then process it, using command:

latex --interaction nonstopmode --shell-escape t.tex

and getting a error:

! Package amsmath Error: Erroneous nesting of equation structures;
(amsmath)                trying to recover with `aligned'.

See the amsmath package documentation for explanation.
Type  H <return>  for immediate help.
 ...

l.10 ...\frac{\sqrt{3}}{2},\\&\cos x=1 \end{align}
                                                   }\right. \Leftrightarrow ...


! Package amsmath Error: Erroneous nesting of equation structures;
(amsmath)                trying to recover with `aligned'.

See the amsmath package documentation for explanation.
Type  H <return>  for immediate help.
 ...

l.10 ... \\& x=2\pi k, k\in\mathbb{Z}. \end{align}
                                                   }\right.
! Undefined control sequence.
<argument> ...+2\pi k, \\& x=2\pi k, k\in \mathbb
                                                  {Z}.
l.10 ... \\& x=2\pi k, k\in\mathbb{Z}. \end{align}
                                                   }\right.
[1] (./t.aux) )
(see the transcript file for additional information)
Output written on t.dvi (1 page, 924 bytes).
Transcript written on t.log.

however, when i use 3th party service for generate picture (any service from google by words "latex 2 png") with same formula - geting a picture without any errors.

I can't make any changes in formula but i need get picture (even formula has any errors)

Answer 1

You mustn't have align environments inside an equation* environment. No exceptions. Trying to compile your code as is simply won't work, and cannot work.

I think that what's needed is to replace the align environments with array environments. By the way, there's no point in loading babel twice with the same language option.

\documentclass[12pt,border=5pt,varwidth]{standalone}
\usepackage{amsmath,amsfonts}
\usepackage[T1,T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[russian]{babel}
\DeclareMathSizes{12}{17.28}{12}{10}
\begin{document}
\begin{equation*}
\renewcommand\arraystretch{2}
\Leftrightarrow \left [ 
\begin{array}{l} \sin x=\frac{\sqrt{3}}{2},\\ 
                 \cos x=1 
\end{array} \right. 
\Leftrightarrow \left [ 
\begin{array}{l} x=\frac{\pi}{3}+2\pi k, \\
                 x=\frac{2\pi}{3}+2\pi k, \\ 
                 x=2\pi k, k\in\mathbb{Z}. 
\end{array} \right.
\end{equation*}
\end{document}