Step 1 :The given expression is \(\cos \beta - \sec \beta\).
Step 2 :We know that \(\sec \beta\) is the reciprocal of \(\cos \beta\), i.e., \(\sec \beta = \frac{1}{\cos \beta}\).
Step 3 :So, we can rewrite the expression as \(\cos \beta - \frac{1}{\cos \beta}\).
Step 4 :To remove the quotient, we can multiply the entire expression by \(\cos \beta\).
Step 5 :This will give us \(\cos^2 \beta - 1\).
Step 6 :Final Answer: The simplified expression in terms of sine and cosine, with no quotients, is \(\boxed{\cos^2 \beta - 1}\). So, the correct answer is A. \(\cos^2 \beta - 1\).