Write each expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression and all functions are of $\theta$ only.
\[
(\sec \theta+\csc \theta)(\cos \theta-\sin \theta)
\]
\[
(\sec \theta+\csc \theta)(\cos \theta-\sin \theta)=
\]

Step 1 ：First, we write each expression in terms of sine and cosine. We have that \(\sec \theta = \frac{1}{\cos \theta}\) and \(\csc \theta = \frac{1}{\sin \theta}\). So, the expression becomes \((\frac{1}{\cos \theta} + \frac{1}{\sin \theta})(\cos \theta - \sin \theta)\).

Step 2 ：Next, we distribute the terms inside the parentheses. This gives us \(\frac{\cos \theta}{\cos \theta} - \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta} - \frac{\sin \theta}{\sin \theta}\).

Step 3 ：Simplifying each term, we get \(1 - \tan \theta + \cot \theta - 1\).

Step 4 ：Finally, we simplify the expression to get \(\cot \theta - \tan \theta\).