Question

Find the value of \( \cos 12^\circ \cdot \cos 24^\circ \cdot \cos 36^\circ \cdot \cos 48^\circ \cdot \cos 72^\circ \cdot \cos 84^\circ \):

• A. \( \frac{1}{32} \)
• B. \( \frac{1}{16} \)
• C. \( \frac{1}{64} \)
• D. \( \frac{1}{128} \)

Hint:

For such trigonometric products, use symmetry and known reduction formulas to simplify the expression.

Answer 1

The Correct Option is C

The given expression involves the product of cosines of angles that are multiples of 12°. This product simplifies using trigonometric identities and leads to the value \( \frac{1}{64} \).