Answer
See the explanation below.
Work Step by Step
To verify the given identity,
${{\cos }^{2}}x-{{\sin }^{2}}x=2{{\cos }^{2}}x-1$
Recall Trigonometric Identity,
${{\sin }^{2}}x+{{\cos }^{2}}x=1$
Use the above identity and solve the left side of the given expression,
$\begin{align}
& {{\cos }^{2}}x-{{\sin }^{2}}x={{\cos }^{2}}x-\left( 1-{{\cos }^{2}}x \right) \\
& =2{{\cos }^{2}}x-1
\end{align}$
Hence, it is proved that the given identity holds true.
