question_answer

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

A)  \[8{{x}^{4}}+4{{x}^{3}}-8{{x}^{2}}-3x+1=0\]

B)  \[8{{x}^{3}}-4{{x}^{2}}+6x+7=0\]

C)  \[{{x}^{3}}-24{{x}^{2}}+18x-164=0\]

D)  \[8{{x}^{3}}+24{{x}^{2}}-8x+164=0\]

E)  None of these