Question

The value of $\cos 6^\circ \sin 24^\circ \cos 72^\circ$ is:

• A. 1/4
• B. -1/8
• C. -1/4
• D. 1/8

Hint:

$\sin 18^\circ = \frac{\sqrt{5}-1}{4}$. This value is frequently used in complex product simplifications.

Answer 1

The Correct Option is D

Step 1: Concept
Use product-to-sum formulas or specific angle identities to simplify the product.

Step 2: Meaning
Rewrite as $1/2 [2 \sin 24^\circ \cos 6^\circ] \cos 72^\circ = 1/2 [\sin 30^\circ + \sin 18^\circ] \cos 72^\circ$.

Step 3: Analysis
Substituting $\sin 30^\circ = 1/2$ and $\sin 18^\circ = \cos 72^\circ$, we get $1/2 [1/2 + \sin 18^\circ] \sin 18^\circ$.

Step 4: Conclusion
Expanding and using standard values for $\sin 18^\circ$ leads to the simplified result of $1/8$.
Final Answer: (D)