\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}

Longitude : $ \lambda $. Latitude : $ \phi $.

\begin{align*}
X' &= \frac{cos\left(\phi\right) \times cos\left(\lambda\right)}{1 + sin\left(\phi\right)} \\
Y' &= \frac{cos\left(\phi\right) \times sin\left(\lambda\right)}{1 + sin\left(\phi\right)} \\
dX' &= - \frac{+ cos\left(\lambda\right) \times d\phi + sin\left(\lambda\right) \times cos\left(\phi\right) \times d\lambda}{1 + sin\left(\phi\right)} \\
dY' &= + \frac{- sin\left(\lambda\right) \times d\phi + cos\left(\lambda\right) \times cos\left(\phi\right) \times d\lambda}{1 + sin\left(\phi\right)} \\
dX &= cos\left(\phi\right) \times d\lambda \\
dY &= d\phi 
\end{align*}


\begin{equation*}
\begin{bmatrix}
dX' \\
dY'
\end{bmatrix}
= 
\frac{1}{1 + sin\left(\phi\right)} \times
\begin{bmatrix}
+ sin\left(\lambda\right) & + cos\left(\lambda\right) \\
+ cos\left(\lambda\right) & - sin\left(\lambda\right) 
\end{bmatrix}
\times
\begin{bmatrix}
dX \\
dY
\end{bmatrix}
\end{equation*}




\end{document}
