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