A) 1/16
B) 0
C) - 1/8
D) -1/16
Correct Answer: D
Solution :
\[\cos \frac{\pi }{5}\cos \frac{2\pi }{5}\cos \frac{4\pi }{5}\cos \frac{8\pi }{5}\] \[=\frac{\sin \frac{{{2}^{4}}\pi }{5}}{{{2}^{4}}\sin \frac{\pi }{5}}=\frac{\sin \frac{16\pi }{5}}{16\,\sin \frac{\pi }{5}}=\frac{\sin \,\left( 3\pi +\frac{\pi }{5} \right)}{16\,\sin \frac{\pi }{5}}\] \[=\frac{-\sin \frac{\pi }{5}}{16\,\sin \frac{\pi }{5}}=-\frac{1}{16}\].
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