How to Align Lines with Comments with other Lines in Math-mode

Question

When I use the \tag command to add a comment in line in math-mode, sometimes that line becomes off-centre and doesn't align with the rest of the equations. Here is example of a code and its output:

\documentclass[a4paper, 11pt, letterpaper]{article}
\usepackage{comment} 
\usepackage{fullpage} 
\usepackage{amsmath,amsthm,amssymb}
\usepackage{mathtools,amsthm}
\begin{document}
\[\mathrm{cosec}^2 (x-200^{\circ}) =2 \tag{$-150 ^{\circ} \leq x-200^{\circ} \leq 150 ^{\circ}$}\]
\[\sin ^2 (x-200 ^{\circ}) = \f 12\]
\[\sin (x-200 ^{\circ}) = \pm \f{1}{\sqrt{2}}\]
\[x-200 ^{\circ} = 45 ^{\circ}, 135 ^{\circ}, -45 ^{\circ}, -135 ^{\circ}\]
\[x= 65^{\circ}, 155 ^{\circ}, 245^{\circ}, 335 ^{\circ}\]
\end{document}

I have tried using the align* environment but then all the equations become a bit off-centre. Also it doesn't look as aesthetic when all the equations are aligned by the equal sign. I would like a solution which still keeps all the equations in the centre of the page.

Thanks for any help!

Answer 1

You can use the flalign* environments, and a medium-sized comment, with the \medmath command, from nccmath. Other solution, nicer in my opinion: two independent aligned environments within gather*:

\documentclass[a4paper, 11pt, letterpaper]{article}
\usepackage{amssymb, amsthm}
\usepackage{mathtools, nccmath}
\DeclareMathOperator{\cosec}{cosec}

\begin{document}

\begin{flalign*}
 & & \cosec ^2 (x-200^{\circ}) & = 2 & & \mathllap{(\medmath{-150 ^{\circ} \leq x-200^{\circ} \leq 150 ^{\circ}})} \\
 & & \sin ^2 (x-200 ^{\circ}) & = \frac12 \\
 & & \sin (x-200 ^{\circ}) & = \pm \frac{1}{\sqrt{2}} \\
 & & x-200 ^{\circ} & = 45 ^{\circ}, 135 ^{\circ}, -\mathrlap{45 ^{\circ}, -135 ^{\circ}} \\
 & & x & = 65^{\circ}, 155 ^{\circ}, \mathrlap{245^{\circ}, 335 ^{\circ}}
\end{flalign*}
\bigskip
\begin{gather*}
\begin{aligned}
  \cosec ^2 (x-200^{\circ}) & = 2 & & \mathrlap{(\medmath{-150 ^{\circ} = \leq x-200^{\circ} \leq 150 ^{\circ}})} \\
  \sin ^2 (x-200 ^{\circ}) & = \frac12 \\
  \sin (x-200 ^{\circ}) & = \pm \frac{1}{\sqrt{2}} 
 \end{aligned}\\[1ex]
\begin{aligned}
  x-200 ^{\circ} & = 45 ^{\circ}, 135 ^{\circ}, - 45 ^{\circ}, -135 ^{\circ} \\
   x & = 65^{\circ}, 155 ^{\circ}, 245^{\circ}, 335 ^{\circ} 
 \end{aligned}
\end{gather*}

\end{document} 

Answer 2

I would keep it simple: there's no need to align at equals signs; moreover, the parenthetical condition is not a comment, but part of the equation.

\documentclass[a4paper,11pt]{article}
\usepackage{amsmath}

\DeclareMathOperator{\cosec}{cosec}
\newcommand{\dg}{^{\circ}}

\begin{document}

\begin{align*}
&\! \cosec ^2 (x-200\dg) = 2 \qquad (-150\dg \leq x-200\dg \leq 150\dg) \\
&\! \sin ^2 (x-200\dg) = \frac12 \\
&\! \sin (x-200\dg) = \pm \frac{1}{\sqrt{2}} \\
& x-200\dg = 45\dg, 135\dg, -45\dg, -135\dg \\
& x = 65\dg, 155\dg, 245\dg, 335\dg
\end{align*}

\end{document}

The \! after = are necessary, because LaTeX inserts a thin space after odd numbered & in align, which would cause misalignment of the operators (not when & is followed by x).

Using a macro such as \dg makes for faster typing and ensures uniformity.

By the way, specifying both a4paper and letterpaper is wrong: use only the option corresponding to your paper format (if it is US Letter, then letterpaper can be omitted because it's the default).