If `x_n=cos+isinpi/(2^n)` , prove that `x_1x_2x_3 x_oo=-1.`

If x_(n)=cos(pi)/(2^(n))+i sin(pi)/(2^(n)), prove that x_(1)x_(2)x_(3)x_(oo)=-1

If x_n =cos ((pi)/(2^(n)))+isin((pi)/(2^(n))) Prove that x_1 x_2…..x_oo=-1

If x_(r)=cos[(pi)/(2^(r))]+iota sin[(pi)/(2^(r))] then,prove that x_(1)*x_(2)*x_(3)...oo=-1

If x_1,x_2,x_3….,x_n are in H.P. prove that x_1x_2+x_2x_3+x_3x_4+……….+x_(n-1)x_n=(n-1)x_1x_n

If x_(n)=cos((pi)/(4^(n)))+i sin((pi)/(4^(n))), then x_(1)*x_(2),x_(3)...............oo

If x_(1),x_(2),x_(3)...x_(n) are in H.P,then prove that x_(1)x_(2)+x_(2)x_(3)+xx x-3x_(4)+...+x_(n-1)x_(n)=(n-1)x_(1)x_(n)

If x in(0,pi/2) and cos x=1/3, then prove that sum_(n=0)^(oo)(cos nx)/(3^(n))=(3(3-cos x))/(10-6cos x+cos^(2)x)

Find 1/x+x=2cos theta, then prove that x^(n)+1/x^(n)=2cos n theta