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-% do-vimlatex-onwrite
-\documentclass[]{article}
-\usepackage[utf8]{inputenc}
-\usepackage{siunitx}
-\usepackage[slovene]{babel}
-\usepackage[inline]{enumitem}
-\usepackage[a4paper, total={7in, 10in}]{geometry}
-\usepackage{hologo}
-\usepackage[hidelinks,unicode]{hyperref}
-\usepackage{datetime}
-\usepackage{tkz-euclide}
-\usepackage{amssymb}
-\usepackage{multicol}
-\usepackage{amsmath}
-% \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=fraction}	% frac način
-% \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=symbol}	% poševnica način
-\sisetup{output-decimal-marker = {,}, quotient-mode=fraction}				% na -1 način
-\settimeformat{hhmmsstime}
-\newcommand{\razhroscevanje}{0}
-\newcommand{\razhroscevanjeg}{0} % grafično razhroščevanje
-\makeatletter
-\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
-\newcommand{\@xslalph}[1]{%
-	\ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
-	\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
-	\or t\or u\or v\or z\or \v{z}
-	\else\@ctrerr\fi%
-}
-\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
-\makeatother
-\title{Trigonometrične formule}
-\author{Anton Luka Šijanec, 3. a}
-\begin{document}
-\maketitle
-% \begin{abstract}
-% Spisek izbranih trigonometričnih izrekov bom kot pripomoček imel na drugem testu pri matematiki v tretjem letniku.
-% \end{abstract}
-% \tableofcontents
-\section{Drugi test}
-\begin{multicols}{2}
-	\begin{tabular}{|c|c|c|c|c|c|}
-		\hline
-		$\measuredangle$	& Rad		& $\sin$		& $\cos$		& $\tan$		& $\cot$		\\
-		\hline
-		$\ang{0}$		& 0		& 0			& 1			& 0			& ne obstaja		\\
-		\hline
-		$\ang{30}$		&$\frac{\pi}{6}$& $\frac{1}{2}$		& $\frac{\sqrt{3}}{2}$	& $\frac{\sqrt{3}}{2}$	& $\sqrt{3}$		\\
-		\hline
-		$\ang{45}$		& $\frac{\pi}{4}$& $\frac{\sqrt{2}}{2}$	& $\frac{\sqrt{2}}{2}$	& 1			& 1			\\
-		\hline
-		$\ang{60}$		& $\frac{\pi}{3}$& $\frac{\sqrt{3}}{2}$	& $\frac{1}{2}$		& $\sqrt{3}$		& $\frac{\sqrt{3}}{3}$	\\
-		\hline
-		$\ang{90}$		& $\frac{\pi}{2}$& 1			& 0			& ne obstaja		& 0			\\
-		\hline
-	\end{tabular}
-	$$\sin^2\alpha+\cos^2\alpha=1$$
-	$$\sin\alpha=\pm\sqrt{1-\cos^2\alpha}$$
-	$$\cos\alpha=\pm\sqrt{1-\sin^2\alpha}$$
-	$\sin, \tan, \cot$ so lihe, $\cos$ je soda.
-	$$\sin\left(-\alpha\right)=-\sin\alpha$$
-	$$\cos\left(-\alpha\right)=\cos\alpha$$
-	$$\sin\left(\frac{\pi}{2}-\alpha\right)=\cos\alpha$$
-	$$\cos\left(\frac{\pi}{2}-\alpha\right)=\sin\alpha$$
-	$$\tan\left(\frac{\pi}{2}-\alpha\right)=\cot\alpha$$
-	$$\sin\left(\alpha\pm\beta\right)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$$
-	$$\cos\left(\alpha\pm\beta\right)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta$$
-	$$\tan\left(\alpha\pm\beta\right)=\frac{\tan\alpha\pm\tan\beta}{1\mp\tan\alpha\tan\beta}$$
-	$$\cot\left(\alpha\pm\beta\right)=\frac{\cot\alpha\cot\beta\mp1}{\cot\beta\pm\cot\alpha}$$
-	$$\sin2\alpha=2\sin\alpha\cos\alpha$$
-	$$\cos2\alpha=cos^2\alpha-\sin^2\alpha=2\cos^2\alpha-1=1-2\sin^2\alpha$$
-	$$\tan2\alpha=\frac{2\tan\alpha}{1-\tan^2\alpha}$$
-	$$\cot2\alpha=\frac{\cot^2\alpha-1}{2\cot\alpha}$$
-	$$\sin3\alpha=3\sin\alpha-4\sin^3\alpha=4\sin\left(\frac{\pi}{3}-\alpha\right)\sin\left(\frac{\pi}{3}+\alpha\right)$$
-	$$\cos3\alpha=4\cos^3\alpha-3\cos\alpha=4\cos\alpha\cos\left(\frac{\pi}{3}-\alpha\right)\cos\left(\frac{\pi}{3}+\alpha\right)$$
-	$$\tan3\alpha=\frac{3\tan\alpha-\tan^3\alpha}{1-3\tan^2\alpha}=\tan\alpha\tan\left(\frac{\pi}{3}-\alpha\right)\tan\left(\frac{\pi}{3}+\alpha\right)$$
-	$$\sin\frac{\alpha}{2}=\pm\sqrt{\frac{1-\cos\alpha}{2}}$$
-	$$\cos\frac{\alpha}{2}=\pm\sqrt{\frac{1+\cos\alpha}{2}}$$
-	$$\tan\frac{\alpha}{2}=\pm\sqrt{\frac{1+\cos\alpha}{1-\cos\alpha}}=\frac{\sin\alpha}{1+\cos\alpha}$$
-	$$2\cos\alpha\cos\beta=\cos\left(\alpha-\beta\right)+\cos\left(\alpha+\beta\right)$$
-	$$2\sin\alpha\sin\beta=\pm\cos\left(\alpha\pm\beta\right)-\cos\left(\alpha\mp\beta\right)$$
-	$$2\sin\alpha\cos\beta=\sin\left(\alpha+\beta\right)+\sin\left(\alpha-\beta\right)$$
-	$$2\cos\alpha\sin\beta=\sin\left(\alpha+\beta\right)-\sin\left(\alpha-\beta\right)$$
-	$$\tan\alpha\tan\beta=1-\frac{\tan\alpha+\tan\beta}{\tan\left(\alpha+\beta\right)}=\frac{\cos\left(\alpha-\beta\right)-\cos\left(\alpha+\beta\right)}{\cos\left(\alpha-\beta\right)+\cos\left(\alpha+\beta\right)}$$
-	$$\sin\alpha\pm\sin\beta=2\sin\left(\frac{\alpha\pm\beta}{2}\right)\cos\left(\frac{\alpha\mp\beta}{2}\right)$$
-	$$\cos\alpha+\cos\beta=2\cos\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$$
-	$$\cos\alpha-\cos\beta=-2\sin\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)$$
-	$$\tan\alpha\pm\tan\beta=\frac{\sin\left(\alpha\pm\beta\right)}{\cos\alpha\cos\beta}$$
-	$$\sin\alpha\cos\alpha=\frac{1}{2}\sin2\alpha$$
-	$$2\cos^2\frac{\alpha}{2}=1+\cos\alpha$$
-	$$2\sin^2\frac{\alpha}{2}=1-\cos\alpha$$
-	$$\tan^2\frac{x}{2}=\frac{1-\cos\alpha}{1+\cos\alpha}$$
-\end{multicols}
-\section{Tretji test}
-\begin{multicols}{2}
-	$$s=\frac{a+b+c}{2} \wedge S=\sqrt{s(s-a)(s-b)(s-c)}$$
-	$$S_\text{trikotnika v izseku}=\frac{r^2\sin\alpha}{2}$$
-	$$\frac{a}{\sin\alpha}=\frac{b}{\sin\beta}=\frac{c}{\sin\gamma}=2R$$
-	$$a^2=b^2+c^2-2bc\cos\alpha$$
-	$$S_\text{paralelograma}=av_a=ab\sin\alpha=\frac{ef}{2}\sin\omega$$
-	$$S_\text{romba}=av=a^2\sin\alpha=\frac{ef}{2}$$
-	$$S_\text{trapeza}=\frac{v(a+c)}{2}$$
-	$$S_\text{deltoida}=\frac{ef}{2}$$
-	$$S_\text{trikotnika}=\frac{ab\sin\gamma}{2}=\frac{av_a}{2}$$
-	$$S_\text{enakostraničnega}=\frac{a^2\sqrt{3}}{4}$$
-	$$\arcsin x+\arccos x=\frac{\pi}{2}$$
-	$$S_\text{trikotnika}=\frac{abc}{4R}=2R^2\sin\alpha\sin\beta\sin\gamma=rs\text{, kjer je } s=\frac{a+b+c}{2}$$
-	$$Diagonal_\text{pravilnega mnogokotnika}=\frac{n(n-3)}{2}$$
-	$$\alpha_\text{pravilnega mnogokotnika}=\frac{n-2}{n}\ang{180}$$
-	$$S_\text{pravilnega mnogokotnika}=\frac{n}{2}R^2\sin\frac{\ang{360}}{n}=
-		na^2\tan\frac{\alpha}{2}\frac{1}{2}=\frac{na^2}{4\tan\frac{\ang{180}}{n}}$$
-	$$\alpha_\text{ene premice}=\arctan k_p$$
-	$$\alpha_\text{med dvema premicama}=\arctan\lvert\frac{k_q-k_p}{1+k_p-k_q}\rvert$$
-	$$D_\text{arcsin}=D_\text{arccos}=[-1; 1] \wedge V_\text{arcsin}=[\ang{-90}; \ang{90}] \wedge V_\text{arccos}=[\ang{0}; \ang{180}]$$
-	$$D_\text{arctan}=D_\text{arccot}=\mathbb{R} \wedge V_\text{arctan}=(\ang{-90}; \ang{90}) \wedge V_\text{arccot}=(\ang{0}; \ang{180})$$
-	$$soda(x)=-soda(x) \wedge liha(-x)=-liha(x)$$
-	$$f(x)\neq-f(x)\nLeftrightarrow f(-x)=-f(x) \text{ in obratno}$$
-	$$f(x)=-f(x) \wedge f(-x)=-f(x) \Leftrightarrow f(x)=0$$
-\end{multicols}
-\section{Zaključek}
-\hologo{LaTeX} izvorna koda dokumenta je objavljena na \url{https://git.sijanec.eu/sijanec/sola-gimb-3}. Za izdelavo dokumenta je potreben \texttt{TeXLive 2020}.
-\if\razhroscevanje1
-\vfill
-\section*{Razhroščevalne informacije}
-Konec generiranja dokumenta \today\ ob \currenttime.
-
-Dokument se je generiral R0qK1KR2 \SI{}{\second}. % aaasecgeninsaaa
-\fi
-\end{document}