Answer
See the explanation below.
Work Step by Step
$\frac{1-\sin \theta }{\cos \theta }=\sec \theta -\tan \theta $
Recall Trigonometric Identities,
$\begin{align}
& \tan \theta =\frac{\sin \theta }{\cos \theta } \\
& \sec \theta =\frac{1}{\cos \theta } \\
\end{align}$
Use the above identities and solve the left side of the given expression,
$\begin{align}
& \frac{1-\sin \theta }{\cos \theta }=\frac{1}{\cos \theta }-\frac{\sin \theta }{\cos \theta } \\
& =\sec \theta -\tan \theta
\end{align}$
Therefore,
$\frac{1-\sin \theta }{\cos \theta }=\sec \theta -\tan \theta $
