Problem

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

Solution

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. \(\cos^2 \beta - 1\).

From Solvely APP
Source: https://solvelyapp.com/problems/19290/

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