Ok, so I have these three equations:
\documentclass[a4,12pt,norsk]{article}
\usepackage[utf8]{inputenc}
\usepackage{babel, amsmath, pgfplots, amsfonts, mathtools}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}%
\DeclarePairedDelimiter\norm{\lVert}{\rVert}%
\makeatletter
\let\oldabs\abs
\def\abs{\@ifstar{\oldabs}{\oldabs*}}
\let\oldnorm\norm
\def\norm{\@ifstar{\oldnorm}{\oldnorm*}}
\makeatother
\begin{document}
\begin{equation}
\abs{\left(\frac{\cos{a}(e^{-b}+e^{b}) + i\sin{a}(e^{-b}-e^{b})}{2}\right)}^2 + \abs{\left(\frac{\cos{a}(e^{-b}-e^{b}) + i\sin{a}(e^{-b}+e^{b})}{2i}\right)}^2 = 1
\end{equation}
\begin{equation}
\left(\frac{\abs{\cos{a}(e^{-b}+e^{b}) + i\sin{a}(e^{-b}-e^{b})}}{\abs{2}}\right)^2 + \left(\frac{\abs{\cos{a}(e^{-b}-e^{b}) + i\sin{a}(e^{-b}+e^{b})}}{\abs{2i}}\right)^2 = 1
\end{equation}
\begin{equation}
\frac{\cos^2{a}(e^{-2b}+2+e^{2b}) + \sin^2{a}(e^{-2b}-2+e^{2b}) +\cos^2{a}(e^{-2b}-2+e^{2b}) +\sin^2{a}(e^{-2b}+2+e^{2b})}{4} = 1
\end{equation}
\end{document}
and they are all taking too much horizontal space. apart from giving me error messsages with "\hbox too full...", it also looks bad. Is there a way to solve this? either making the equation less spaced or "moving" the equations backwards, so they are more centered?
\abs
?