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Thanks for the help. I don't see why the functions aren't aligning perfectly with uniform spacing.

\documentclass[11pt]{article}

\begin{document}

\DeclareMathOperator{\csch}{csch}
\DeclareMathOperator{\sech}{sech}




\begin{align*}
\sinh(x)= \frac{e^x-e^{-x}}{2}, &   \qquad \cosh(x)= \frac{e^x+e^{-x}}{2}, & \tanh(x)=  \frac{\sinh(x)}{\cosh(x)} \\
\csch(x)= \frac{1}{\sinh(x)}, & \qquad  \sech(x)= \frac{1}{\cosh(x)}, & \coth(x)= \frac{1}{\tanh(x)}. 
\end{align*}

\end{document}
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Thanks for adding the example. You can format code by selecting it and clicking on the {} icon. – Alan Munn Mar 9 at 23:49
    
But your code doesn't compile. – Alan Munn Mar 9 at 23:57
    
The main section \begin{align*} ... \end{align*} aligns well, but needs to have some corrections in defining \csch and \sech – Leucippus Mar 10 at 0:03
2  
Hi! Welcome to the site :) How is \csch defined here? It's good to provide a complete but Minimal Working Example. In other words, we should be able to copy and paste all your code and compile it exactly as it is and see exactly what you see, so you need to include everything that's needed to allow us to do that. But ideally nothing more. So it's good that you've stripped away what isn't necessary in your example, but I think you've also stripped away some things that are necessary – Au101 Mar 10 at 0:12
up vote 11 down vote accepted

You're probably after an alignment around =:

enter image description here

\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator{\csch}{csch}
\DeclareMathOperator{\sech}{sech}

\begin{document}

\begin{align*}
  \sinh(x) &= \frac{e^x-e^{-x}}{2}, & \cosh(x) &= \frac{e^x+e^{-x}}{2}, & \tanh(x) &= \frac{\sinh(x)}{\cosh(x)} \\
  \csch(x) &= \frac{1}{\sinh(x)},   & \sech(x) &= \frac{1}{\cosh(x)},   & \coth(x) &= \frac{1}{\tanh(x)}. 
\end{align*}

\end{document}

Every odd-numbered & provides a right-left alignment. Every even-numbered & adds a horizontal gap or spread between the components.

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