Can someone please check this for me thanks.

Question is $\displaystyle \cos ec(\cos ^{ - 1} (\frac{1}{y})) = $

This is what I worked it to be

$\displaystyle

\begin{array}{l}

{\rm let }\theta = \cos ^{ - 1} (\frac{1}{y}) \\

\cos \theta = \frac{1}{y} \\

\cos ^2 \theta + \sin ^2 \theta = 1 \\

(\frac{1}{y})^2 + \sin ^2 \theta = 1 \\

\sin ^2 \theta = 1 - (\frac{1}{y})^2 \\

\sin \theta = \sqrt {1 - \left( {\frac{1}{y}} \right)^2 } \\

\cos ec\theta = \frac{1}{{\sin \theta }} = \frac{1}{{\sqrt {1 - \left( {\frac{1}{y}} \right)^2 } }} \\

\end{array}

$

Is it right?