Question

Evaluate \( \dfrac{\cos 60^\circ + 1}{\cos 60^\circ - 1} \).

• A. \(2\)
• B. \(-2\)
• C. \(3\)
• D. \(-3\)

Hint:

Memorize \(\cos 60^\circ=\tfrac{1}{2}\) and \(\sin 30^\circ=\tfrac{1}{2}\); they simplify many trig ratios instantly.

Answer 1

The Correct Option is D

Step 1: Use the exact value of \(\cos 60^\circ\).
\(\cos 60^\circ = \dfrac{1}{2}\).
Step 2: Substitute and simplify.
\[ \dfrac{\cos 60^\circ + 1}{\cos 60^\circ - 1} = \dfrac{\tfrac{1}{2}+1}{\tfrac{1}{2}-1} = \dfrac{\tfrac{3}{2}}{-\tfrac{1}{2}} = -3. \]
Step 3: Conclude.
Hence, the required value is \(-3\).