Question

Let \( s_n = \cos\left(\frac{n\pi}{10}\right) \), \( n=1,2,3, \ldots \). Then the value of \( \frac{s_1s_2\cdots s_{10}}{s_1+s_2+\cdots+s_{10}} \) is equal to:

• A. \( \frac{1}{\sqrt{2}} \)
• B. \( \frac{\sqrt{3}}{2} \)
• C. \( 2\sqrt{2} \)
• D. \( 0 \)
• E. \( \frac{1}{2} \)

Hint:

Whenever you see a long product of trigonometric terms, check for "special angles" like $90^\circ$ for cosine or $0^\circ/180^\circ$ for sine that might zero out the whole expression.

Answer 1

The Correct Option is D