\input amstex
$$\eqalign{
\frac{1}{\sqrt{
  \frac{\sin\frac{\pi}{2}}
       {\cos\frac{\pi}{2}}
}}&=\left(\sqrt{\frac{\sin\frac{\pi}{2}}
{\cos\frac{\pi}{2}}}\right)^{-1}\overset{\text{(*)}}\to{=}%
\sqrt{\left(\frac{\sin\frac{\pi}{2}}
{\cos\frac{\pi}{2}}\right)^{-1}}=\cr
&\sqrt{\frac{\cos\frac{\pi}{2}}
{\sin\frac{\pi}{2}}}=\sqrt{\frac{0}{1}}=0
}$$
\bye