Prove that the roots of the equation
`8x^(2)-4x^(2)-4x+1=0` are `cos. (pi)/(7), cos. (3pi)/(7), cos. (5pi)/(7)` and hence, show that `sec. (pi)/(7) + sec. (3pi)/(7) + sec. (5pi)/(7) = 4` and deduce the equation whose roots are `tan^(2). (pi)/(7)+sec. (3pi)/(7)+sec. (5pi)/(7)=4` and deduce the equation whose roots are `tan^(2). (pi)/(7) , tan^(2) . (3pi)/(7), tan^(2). (5pi)/(7)`.

Answer

Required equation is , `z^(3)-21z^(2)+35z-7=0` whose roots are
`tan^(2). (pi)/(7), tan^(2). (3pi)/(7), tan^(2). (5pi)/(7)`