Answer
Verified below.
Work Step by Step
We have $\frac{1-{{\tan }^{2}}x}{1+{{\tan }^{2}}x}=\cos 2x $
By evaluating the left side,
$\begin{align}
& \text{Left side}=\frac{1-{{\tan }^{2}}x}{1+{{\tan }^{2}}x} \\
& =\frac{{{\cos }^{2}}x-{{\sin }^{2}}x}{{{\cos }^{2}}x+{{\sin }^{2}}x} \\
& =\frac{\cos 2x}{1} \\
& =\cos 2x
\end{align}$
Therefore, $\text{left side = right side}$. Thus, we can say that the identity is true.
Hence, verified.
