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\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}

\thispagestyle{empty}
\begin{document}
\begin{equation}
  P(x)=\cos^2\theta \frac{1}{\sqrt{2\pi\sigma_1^2}}e^{-\frac{(x-x_{0,1})^2}{2\sigma_1^2}}+\sin^2\theta \frac{1}{\sqrt{2\pi\sigma_2^2}}e^{-\frac{(x-x_{0,2})^2}{2\sigma_2^2}}
\end{equation}
\end{document}