#### Answer

The value of the ${{\sin }^{2}}\alpha $ is $\frac{1-\cos \,2\alpha }{2}$.

#### Work Step by Step

In order to find the value of ${{\sin }^{2}}\alpha $, the power reducing formula is used that is as shown below:
${{\cos }^{2}}\alpha =1-2{{\sin }^{2}}\alpha $
The aforementioned formula is proved in the earlier problems.
Solve the aforementioned formula on the left side for the ${{\sin }^{2}}\alpha $:
$\begin{align}
& 2{{\sin }^{2}}\alpha =1-\cos 2\alpha \\
& {{\sin }^{2}}\alpha =\frac{1-\cos 2\alpha }{2}
\end{align}$
Hence, the value of the ${{\sin }^{2}}\alpha $ is $\frac{1-\cos \,2\alpha }{2}$.