Convert documentation of improper styles from images to mathjax

\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}

  E & = & E_i + E_{aa} \\

  E_i & = & K [ \frac{\chi_{ijkl} + \chi_{kjli} + \chi_{ljik}}{3} - \chi_0 ]^2 \\

  E_{aa} & = & M_1 (\theta_{ijk} - \theta_1) (\theta_{kjl} - \theta_3) + \\

  & & M_2 (\theta_{ijk} - \theta_1) (\theta_{ijl} - \theta_2) + \\

  & & M_3 (\theta_{ijl} - \theta_2) (\theta_{kjl} - \theta_3)

\end{eqnarray*}

\end{document}

 No newline at end of file

\documentclass[12pt]{article}

\begin{document}

$$

  E = \frac{1}{2} K \cos^2{\left(\chi - \chi_0\right)}

$$

\end{document}