Answer
The required value of the ${{\tan }^{2}}y$ is $\frac{1-\cos \,2y}{1+\cos \,2y}$.
Work Step by Step
In order to find the value of ${{\tan }^{2}}y$, the power reducing formula is used that is as given below:
$\begin{align}
& {{\tan }^{2}}y=\frac{{{\sin }^{2}}y}{{{\cos }^{2}}y} \\
& =\frac{\frac{1-\cos 2y}{2}}{\frac{1+\cos 2y}{2}} \\
& =\frac{1-\cos 2y}{{}}\times \frac{{}}{1+\cos 2y} \\
& =\frac{1-\cos 2y}{1+\cos 2y}
\end{align}$
