Question

If $s_n=\cos \left(\frac{n\pi }{10}\right),n=1,2,3,.....$, then the value of $\frac{s_1{s}_2...,s_{10}}{s_1+s_2+.....+s_{10}}$ is equal to

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

Answer 1

Answer: (D)

$0$

$s_n=\cos (\frac{n\pi }{10})$

$⟹s_5=\cos \left(\frac{\pi }{2}\right)=0$
So equation $\frac{s_1{s}_2...,s_{10}}{s_1+s_2+.....+s_{10}}=s_5\times \frac{s_1{s}_2..,s_4,s_6..,s_{10}}{s_1+s_2+.....+s_{10}}$
$s_5\times \frac{s_1{s}_2..,s_4,s_6..,s_{10}}{s_1+s_2+.....+s_{10}}=0$
Hence answer is D