Question

I need to simplify and write this trig expression as a single function

Answer 1

`(\cos U\cdot\sec U)/(\tan U)`

To simplify this expression we will use trigonometric identities

`\begin{gathered} \sec U=(1)/(\cos U) \\ \tan U=(sinU)/(\cos U) \end{gathered}`

Replacing the identities in the equation:

`\begin{gathered} =(\cos U\cdot(1)/(\cos U))/(\tan U) \\ =(1)/(\tan U) \\ =(1)/((sinU)/(\cos U)) \\ =(\cos U)/(sinU) \end{gathered}`

When they ask to simplify it is to leave it in terms of sines and cosines if possible. So the answer is

`(\cos U\cdot\sec U)/(\tan U)=(\cos U)/(sinU)`