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我排版代码时出现 2 个问号

tag-icon • tag-icon math-mode amsmath greek
我排版代码时出现 2 个问号

仅在最后一行，我的输出在最后一个分数中的 \beta 之前显示为 ??。

    \usepackage{amsmath}
\usepackage{amstext}
\usepackage{amssymb}
\usepackage{float}
\usepackage{graphicx}
\graphicspath{ {images/} }
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}


\begin{document}
\maketitle % showing both title and author, plus and automatic date

\includegraphics{proof9}

Applying trigonometric functions to the larger right triangle, we get
\begin{align}
\sin(\alpha+\beta)&=\frac{\sin\beta+a}{\cos\alpha+b}\\
&=\frac{\sin\beta+\frac{\sin\alpha}{\cos(\alpha+\beta)}}{\cos\alpha+\sin\alpha\frac{\sin(\alpha+\beta)}{\cos(\alpha+\beta)}}\\
\textit{and}\\
\cos(\alpha+\beta)&=\frac{\cos\beta}{\cos\alpha+b}\\
&=\frac{\cos\beta}{\cos\alpha+\sin\alpha\frac{\sin(\alpha+‌​\beta)}{\cos(\alpha+‌​\beta)}}.
\end{align}
\end{document}

答案1

测试版之前有零宽度字符。

如果你将该段文本粘贴到（例如）这里

https://w3c.github.io/xml-entities/unicode-names.html

你会看见

  U+0061 LATIN SMALL LETTER A     a
  U+006c LATIN SMALL LETTER L     l
  U+0070 LATIN SMALL LETTER P     p
  U+0068 LATIN SMALL LETTER H     h
  U+0061 LATIN SMALL LETTER A     a
  U+002b PLUS SIGN     + \mathplus +
  U+200c ZERO WIDTH NON-JOINER     ‌
  U+200b ZERO WIDTH SPACE     ​ ​ ​ ​ ​
  U+005c REVERSE SOLIDUS     \ \backslash \textbackslash
  U+0062 LATIN SMALL LETTER B     b
  U+0065 LATIN SMALL LETTER E     e
  U+0074 LATIN SMALL LETTER T     t
  U+0061 LATIN SMALL LETTER A     a

表明该位置有 U+200C 和 U+200B，需要删除。

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