Here is my code:
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\documentclass[a4paper, fleqn]{article}
\usepackage{amsmath}
\usepackage[latin1]{inputenc}
\title{Lösningsförslag till några problem på s.179}
\date{}
\author{}
\topmargin -1.0cm
\textheight 23.7cm
\oddsidemargin -0.5cm
\evensidemargin -0.5cm
\textwidth 17cm
\begin{document}
\maketitle
\section*{5335}
Visa att
\[\begin{aligned}[t]
\frac{1}{1-\sin v}+\frac{1}{1+\sin v} &= \frac{2}{\cos^2 v} \\
\frac{1+\sin v}{1-\sin v}+\frac{1+\sin v}{1+\sin v} &= \frac{2(1+\sin v)}{\cos^2 v} \\
\frac{1+\sin v}{1-\sin v}+1 &= \frac{2(1+\sin v)}{\cos^2 v} \\
1+\sin v+1-\sin v &= \frac{2(1+\sin v)(1-\sin v)}{\cos^2 v} \\
2 &= \frac{2(1-\sin^2v)}{\cos^2v} \\
2 &= 2
\end{aligned}\]
\end{document}