Question

The value of $\cos \frac{\pi }{2^2}.\cos \frac{\pi }{2^3}........\cos \frac{\pi }{2^{10}}.\sin \frac{\pi }{2^{10}}$ is :

• A. $\frac{1}{256}$
• B. $\frac{1}{2}$
• C. $\frac{1}{512}$
• D. $\frac{1}{1024}$

Answer 1

Answer: (C)

$2\sin \frac{\pi }{2^{10}}\cos \frac{\pi }{2^{10}}.......\cos \frac{\pi }{2^2}$
$\frac{1}{2^9}\sin \frac{\pi }{2}=\frac{1}{512}$