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