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Beim Versuch, einem Dokument mathematische oder Zahlen hinzuzufügen, werden anscheinend alle drei Elemente gequetscht. Dadurch sehen die Dokumente inkonsistent aus und ich frage mich, ob es dafür eine Lösung gibt.
\documentclass[letterpaper,12pt]{article}
\usepackage{newfloat}
\usepackage[showframe, left=1.5cm, right=1.5cm, top=1.5cm, bottom=1.5cm]{geometry}
\usepackage{titling}
\usepackage{indentfirst}
\usepackage{fancyhdr}
\usepackage{microtype}
\usepackage{unicode-math}
\setmainfont{Times New Roman}[Ligatures=TeX]
\setmathfont{STIX Two Math}
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\renewcommand{\arraystretch}{1.5}
% }
\title{Title of Document}
\author{Author Name Generic}
\date{\today}
\begin{document}
\maketitle
\end{document}
Code mit Mathematik zum Vergleichen
% {
\documentclass[letterpaper,12pt]{article}
\usepackage{newfloat}
\usepackage[showframe, left=1.5cm, right=1.5cm, top=1.5cm, bottom=1.5cm]{geometry}
\usepackage{titling}
\usepackage{indentfirst}
\usepackage{fancyhdr}
\usepackage{microtype}
\usepackage{siunitx}
\usepackage{stackengine}
\usepackage{cancel}
\usepackage{unicode-math}
\setmainfont{Times New Roman}[Ligatures=TeX]
\setmathfont{STIX Two Math}
\setlength{\droptitle}{-2cm}
\renewcommand{\maketitlehookb}{\vspace{-1cm}}
\renewcommand{\maketitlehookd}{\vspace{-.5cm}}
\renewcommand{\arraystretch}{1.5}
% }
\title{Title of Document}
\author{Author Name Generic}
\date{\today}
\begin{document}
\maketitle
Identities \newline
The Sum and Difference Identities
\begin{gather}
\cos(\alpha - \beta) = \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta)\\
\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta)\\
\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)\\
\sin(\alpha - \beta) = \sin(\alpha)\cos(\beta) - \cos(\alpha)\sin(\beta)
\end{gather}
\textbf{Example 1:} Evaluating a Trigonometric Function \newline
A. Find the exact value of $\displaystyle \sin\left(\dfrac{\pi}{12}\right)$
\begin{align}
\frac{\pi}{12} &= \frac{4\pi}{12} - \frac{3\pi}{2}\\
&= ~ \frac{\pi}{3} ~~~~~~~\frac{\pi}{4}
\end{align}
\begin{align}
&\sin\left(\frac{\pi}{12}\right) = \sin\left(\frac{\pi}{3} - \frac{\pi}{4}\right)\\
&= \sin \left(\frac{\pi}{3}\right)\cos\left(\frac{\pi}{4}\right) - \cos\left(\frac{\pi}{3}\right)\sin\left(\frac{\pi}{4}\right)\\
&= \left(\frac{\sqrt{2}}{2}\right) \left(\frac{\sqrt{2}}{2}\right) - \left(\frac{1}{2}\right) \left(\frac{\sqrt{2}}{2}\right)\\
&= \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} = \frac{\sqrt{6} - \sqrt{2}}{4}
\end{align}
B. Find the exact value of $\cos(\ang{75}).$
\begin{align}
&\cos(\overset{\alpha}{\ang{30}} + \overset{\beta}{\ang{45}})\\
&= \cos(\ang{30})\cos(\ang{45})-\sin(\ang{30})\sin(\ang{45})\\
&= \left(\frac{\sqrt{3}}{2}\right) \left(\frac{\sqrt{2}}{2}\right) - \left(\frac{1}{2}\right) \left(\frac{\sqrt{2}}{2}\right)\\
&= \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} = \frac{\sqrt{6} - \sqrt{2}}{4}
\end{align}
\textbf{Example 2}: Proving a Cofunction Identity \newline
Use a difference formula to prove the cofunction identity:
\begin{gather}
\cos \left(\frac{\pi}{2} - x\right) = \sin(x)
\end{gather}
\begin{align}
\cos \left(\frac{\pi}{2} - x\right) &= \cos \overset{0}{\left(\frac{\pi}{2}\right)} \cos(x) + \sin \overset{1}{\left(\frac{\pi}{2}\right)} \sin(x)\\
&= 0 \ast \cos(x) + 1 \ast \sin(x)\\
&= \sin(x)
\end{align}
\textbf{Example 3:} Solve
\[
\sin\overset{\alpha}{(x)}\sin\overset{\beta}{(2x)} + \cos\overset{\alpha}{(x)}\cos\overset{\beta}{(2x)} = \frac{\sqrt{3}}{2}
\]
Recall: $\cos(-x) = \cos(x)$
\begin{align}
\cos (x - 2x) &= \frac{\sqrt{3}}{2}\\
&\cos (-x) = \frac{\sqrt{3}}{2}\\
&\cos x = \frac{\sqrt{3}}{2}\\
&x = \frac{\pi}{6} + 2 \pi k\\
&x = \frac{11 \pi}{6} + 2 \pi k
\end{align}
Identities \newline
The Product to Sum Identities
\begin{gather}
\sin(\alpha)\cos(\beta) = \frac{1}{2}(\sin(\alpha + \beta) + \sin(\alpha - \beta))\\
\sin(\alpha)\cos(\beta) = \frac{1}{2}(\cos(\alpha - \beta) + \cos(\alpha + \beta))\\
\cos(\alpha)\cos(\beta) = \frac{1}{2}(\cos(\alpha + \beta) + \cos(\alpha - \beta))
\end{gather}
\textbf{Example 4:} Write $\sin\overset{\alpha}{(2t)}\sin\overset{\beta}{(4t)}$ as a sum or difference
\begin{align}
&= \frac{1}{2}(\cos(2t - 4t) - \cos(2t + 4t))\\
&= \frac{1}{2}(\cos(-2t) - \cos (6t))\\
&= \frac{1}{2} (\cos(2t) - \cos (6t))
\end{align}
Identities \newline
The Sum to Product Identities
\begin{align}
\sin(u) + \sin(v) = 2\sin\left(\frac{u + v}{2}\right)\cos
\left(\frac{u - v}{2}\right)\\
\sin(u) - \sin(v) = 2\sin\left(\frac{u - v}{2}\right)\cos
\left(\frac{u + v}{2}\right)\\
\cos(u) + \cos(v) = 2\cos\left(\frac{u + v}{2}\right)\cos
\left(\frac{u - v}{2}\right)\\
\cos(u) - \cos(v) = 2\cos\left(\frac{u - v}{2}\right)\cos
\left(\frac{u + v}{2}\right)
\end{align}
\textbf{Example 5:} Evaluate $\cos\stackon{(\ang{15})}{u} - \cos\stackon{(\ang{75})}{v}$ \newline
Recall: $\sin(-30) = -\sin(30)$
\begin{align}
&-2 \sin \left(\frac{\ang{15} + \ang{75}}{2}\right) \sin\left(\frac{\ang{15} - \ang{75}}{2}\right)\\
&+ 2 \sin (\ang{45}) ~ \sin (\ang{30})\\
&= \cancel{2} \left(\frac{\sqrt{2}}{\cancel{2}}\right) \left(\frac{1}{2}\right) = \left(\frac{\sqrt{2}}{2}\right)
\end{align}
\end{document}
Wenn irgendjemand dabei helfen könnte, wäre das eine große Hilfe