Splitting longer equation to multiple lines having various types of brackets

I have tried to type the following equation which is long and has many brackets (types and numbers).

$$\begin{split} \tau_{\xi\eta} & = \frac{1}{2}\,\frac{\left(1-\lambda\right)\,\sigma_{0}\,e^{2\xi_{o}}}{\left(\,cosh\,2\xi - \,cos\,2\eta \right)^2} \left\lbrace \left(cosh\,2\xi - cos\,2\eta\right)\left[ sinh\,2\,(\xi-\xi_{o}) \right. \\ &\quad \left. \times sin\,2(\eta-\beta) - sinh\,2\xi_{o}\,sin\,2\beta \right] - \left[sin\,2\beta\,sinh\,2\xi (cos\,2\eta \right. \\ &\quad \left. - cosh\,2\xi_{o}) + cos\,2\beta\,sin\,2\eta(cosh\,2\xi_{o}-cosh\,2\xi)\right] \right\rbrace \\ &\quad - \frac{1}{2}\,\frac{\left(1+\lambda\right)\,\sigma_{0}}{\left(\,cosh\,2\xi - \,cos\,2\eta \right)^2}\times sin\,2\eta (cosh\,2\xi_{o}-cosh\,2\xi) \end{split}$$


It is resulting in the following equation with errors.

I greatly appreciate insight into where things are going wrong.

• It is good practice to space commands on both sides. Use \left( \eta \right) \, and not \left(\eta\right)\,, e.g. Mar 28, 2021 at 9:54

1 Answer

Virtually all of the \left and \right directives in your code do absolutely nothing useful; in fact, their multitudinous presence makes it quite difficult to figure out which ones actually do something useful -- and replace only the useful ones with \Bigl, \bigl, \bigr, and \Bigr, respectively.

Also, do please write \sin, \sinh, \cos, and \cosh, i.e., do please use the blackslash characters. Not only will this make for better-looking output, it also lets you get rid of all 20+ [!] \, (thinspace) directives.

Finally, I'd place the four & alignment specifiers so that the \frac{1}{2} directives in rows 1 and 4 are aligned vertically.

\documentclass{article}
\usepackage{amsmath} % for 'split' env.
\begin{document}
$$\begin{split} \tau_{\xi\eta} &=\frac{1}{2}\frac{(1-\lambda)\sigma_{0} e^{2\xi_{0}}}{(\cosh 2\xi - \cos 2\eta )^2} \Big\lbrace (\cosh2\xi - \cos2\eta) \bigl[ \sinh2(\xi-\xi_{o}) \\ &\qquad \times \sin 2(\eta-\beta) - \sinh2\xi_{o}\sin 2\beta \bigr] - \bigl[\sin 2\beta\sinh2\xi (\cos2\eta \\ &\qquad - \cosh2\xi_{o}) + \cos2\beta\sin 2\eta(\cosh2\xi_{o} - \cosh2\xi)\bigr] \smash{\Big\rbrace} \\ % '\smash' is optional &-\frac{1}{2}\frac{(1+\lambda)\sigma_{0}}{(\cosh 2\xi - \cos 2\eta )^2} \sin 2\eta (\cosh2\xi_{o}-\cosh2\xi) \end{split}$$
\end{document}

• Wonderful inputs. I created 2 other longer equations like the one I shared here. I will now modify those as well following your suggestions. Thank you. Mar 28, 2021 at 10:48