1.

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»


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)`


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