Answer
See the explanation given below.
Work Step by Step
Let us consider the left side of the expression:
$\begin{align}
& \sec \theta -\cos \theta =\frac{1}{\cos \theta }-\frac{\cos \theta }{1} \\
& =\frac{1-{{\cos }^{2}}\theta }{\cos \theta } \\
& =\frac{{{\sin }^{2}}\theta }{\cos \theta } \\
& =\frac{\sin \theta }{\cos \theta }\sin \theta
\end{align}$
Finally, use the identities $\sec \theta =\frac{1}{\cos \theta },\ \tan \theta =\frac{\sin \theta }{\cos \theta }$. Therefore, $\sec \theta -\cos \theta =\tan \theta \sin \theta $
Thus, the left side of the expression is equal to right side.
