question_answer

Directions: Based on the following paragraph.

If \[\cos \,\,\frac{\pi }{7},\] \[cos\,\,\frac{3\pi }{7},\] \[\cos \,\,\frac{5\pi }{7}\] are the roots of the equation \[8{{x}^{3}}-4{{x}^{2}}-4x+1=0\]

Find the value of \[\sin \,\,\frac{\pi }{17}\,\,\sin \,\,\frac{3\pi }{14}\,\,\sin \,\,\frac{5\pi }{14}\]

A)  \[\frac{1}{4}\]                         

B)  \[\frac{1}{8}\]

C)  \[\frac{\sqrt{7}}{4}\]                            

D)  \[\frac{\sqrt{7}}{8}\]

E)  None of these