Answer
The required value is $\frac{\sqrt{3}}{2}$
Work Step by Step
We have the double angle formulas, ${{\cos }^{2}}\theta -{{\sin }^{2}}\theta =\cos 2\theta $. Therefore, applying the formula in the given expression where $\theta ={{15}^{\circ }}$, we get:
$\begin{align}
& {{\cos }^{2}}15-{{\sin }^{2}}15=\cos \left( {{2.15}^{\circ }} \right) \\
& =\cos \left( {{30}^{\circ }} \right) \\
& =\frac{\sqrt{3}}{2}
\end{align}$
Hence, the required value is $\frac{\sqrt{3}}{2}$
