[tex]\frac{\cos U\cdot\sec U}{\tan U}[/tex]
To simplify this expression we will use trigonometric identities
[tex]\begin{gathered} \sec U=\frac{1}{\cos U} \\ \tan U=\frac{sinU}{\cos U} \end{gathered}[/tex]
Replacing the identities in the equation:
[tex]\begin{gathered} =\frac{\cos U\cdot\frac{1}{\cos U}}{\tan U} \\ =\frac{1}{\tan U} \\ =\frac{1}{\frac{sinU}{\cos U}} \\ =\frac{\cos U}{sinU} \end{gathered}[/tex]
When they ask to simplify it is to leave it in terms of sines and cosines if possible. So the answer is
[tex]\frac{\cos U\cdot\sec U}{\tan U}=\frac{\cos U}{sinU}[/tex]
