\documentclass{article}
\begin{document}
\setcounter{equation}{5}
\begin{eqnarray}
\arcsin x & = & -\arcsin(-x) = \frac{\pi}{2} - \arccos x = 
	       \left[\arccos\sqrt{1-x^2}\,\right]\nonumber\\
	  & = & \arctan\frac{x}{\sqrt{1-x^2}} =
	       \left[\mbox{\rm arccot}\frac{\sqrt{1-x^2}}{x}\right]
\end{eqnarray}
\begin{eqnarray}
\lefteqn{f(x+h,y+k) = f(x,y) + \left\{\frac{\partial f(x,y)}{\partial x}h +
    \frac{\partial f(x,y)}{\partial y}k\right\}}\nonumber\\
    &&\mbox{} + \frac{1}{2}\left\{\frac{\partial^2f(x,y)}{\partial x^2}h^2
      + 2\frac{\partial^2f(x,y)}{\partial x\partial y}kh
      +  \frac{\partial^2f(x,y)}{\partial y^2}k^2\right\}\\
    &&\mbox{} + \frac{1}{6}\{\cdots\} + \cdots + \frac{1}{n!}\{\cdots\} + R_n
    \nonumber
\end{eqnarray}
\end{document}