z0 is a root of the equation `z^ncos[thetao]`+`z^[n-1]cos[theta1]`+`z^[n-2]cos[theta2]`+.......+`z^ncos[theta[n-1]]+costheta[n]`=2 where `Theta[i] in R` then

z0is a root of the equation z^(n)cos[theta o]+z^(n-1)cos[theta1]+z^(n-2)cos theta[theta2]+......+z^(n)cos[theta[n-1]]+cos theta[n]=2 where Theta[i]in R

zo is one of the roots of the equation z^(n)cos theta0+z^(n-1)cos theta2+......+z cos theta(n-1)+cos theta(n)=2, where theta in R, then (A)|z0| (1)/(2)(C)|z0|=(1)/(2)

All the roots of equation z^n costgheta_0 +z^(n-1) costheta_1 +z^(n-2) costheta_2+…+costheta_n=2, when theta_0, theta_1, theta_2, ……theta_n epsilon R lie (A) on the line Re[(3+4i)z]=0 (B) inside the circel |z|=1/2 (C) outside the circle |z|= 1/2 (D) on the circle |z|= 1/2

If z=sin theta-i cos theta then for any integer n

Solution of the equation sin (sqrt(1+sin 2 theta))= sin theta + cos theta is (n in Z)

y=sin^(2)theta+cos ec^(2)theta,theta!=n pi n in z then

If |2 sin theta-cosec theta| ge 1 and theta ne (n pi)/2, n in Z , then

If z=cos theta+i sin theta is a root of the equation a_(0)z^(n)+a_(2)z^(n-2)+...+a_(n-1)z+a_(n)=0, then prove that a_(0)+a_(1)cos theta+a_(2)cos2 theta+...+a_(n)cos n theta=0a_(1)sin theta+a_(2)sin2 theta+...+a_(n)sin n theta=0

Show that there is no complex number such that |z|le1/2 and z^(n)sin theta_(0)+z^(n-1)sintheta_(2)+....+zsintheta_(n-1)+ sintheta_(n)=2 where theta,theta_(1),theta_(2),……,theta_(n-1), theta_(n) are reals and n in Z^(+) .