If `z=costheta+isintheta` is a root of the equation `a_0z^n+a_2z^(n-2)++a_(n-1)z^+a_n=0,` then prove that `a_0+a_1costheta+a_2^cos2theta++a_ncosntheta=0` `a_1"sin"theta+a_2^sin2theta++a_nsinntheta=0`

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

If z=costheta+isintheta , then (z^(2n)-1)/(z^(2n)+1)

Prove that (1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)=2^(n+1)cos^(n)((theta)/(2))cos((ntheta)/(2))

If z=(costheta+isintheta) , show that z^(n)+(1)//(z^(n))=2cosntheta and z^(n)-(1)(z^(n))=2isinntheta

If z= costheta+isintheta , then the value of (z^(2n)-1)/(z^(2n)+1) (A) i tan n theta (B) tan n theta (C) icot n theta (D) -i tan n theta

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

If n is an integer and z=cos theta+i sin theta , then (z^(2 n)-1)/(z^(2 n)+1)=