Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression.
\[
\cos \beta-\sec \beta
\]
Choose the correct answer below.
A. $\cos ^{2} \beta-1$
B. $\cos ^{2} \beta$
C. $\sin ^{2} \beta$
D. $-\cos ^{2} \beta \cot ^{2} \beta$
E. $-\sin \beta \tan \beta$
F. 1
Answer
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. \(\cos^2 \beta - 1\).
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. \(\cos^2 \beta - 1\).
