参考：Latex大括号及多行公式
方法一：
\begin{equation}
\begin{cases}
\delta_1 = sin^2{\left ( \frac{\varphi_2 - \varphi_1}{2} \right )}, \\
\delta_2 = cos(\varphi_1) \cdot cos(\varphi_2) \cdot sin^2{\left ( \frac{\lambda_2 - \lambda_1}{2} \right )}, \\
D = 2 \cdot R \cdot arcsin \left ( \sqrt{\delta_1 + \delta_2} \right),
\end{cases}
\end{equation}
方法二：
\begin{equation}
\left\{
\begin{array}{lr}
\delta_1 = sin^2{\left ( \frac{\varphi_2 - \varphi_1}{2} \right )}, & \\
\delta_2 = cos(\varphi_1) \cdot cos(\varphi_2) \cdot sin^2{\left ( \frac{\lambda_2 - \lambda_1}{2} \right )}, & \\
D = 2 \cdot R \cdot arcsin \left ( \sqrt{\delta_1 + \delta_2} \right), &
\end{array}
\right.
\end{equation}
效果：（上面代码位置调换了）