Question:
The value of $\cos \frac{\pi}{2^{2}} \cdot \cos \frac{\pi}{2^{3}} \cdot \ldots \cdot \cdot \cdot \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ is :
Correct Option: , 3
Solution:
$2 \sin \frac{\pi}{2^{10}} \cos \frac{\pi}{2^{10}} \ldots \ldots \cdot \cos \frac{\pi}{2^{2}}$
$\frac{1}{2^{9}} \sin \frac{\pi}{2}=\frac{1}{512}$
Option (3)