似乎在尝试向文档添加数学或数字时,这三个部分都会被挤压。这会使文档看起来不一致,我想知道是否有办法解决此问题。
\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}
\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
\end{document}
用数学代码进行比较
% {
\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}
如果有人能帮忙,那将是一个巨大的帮助