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

If x_(n)=cos(pi/2^(n))+isin(pi/2^(n)), n in N then x_(1),x_(2),x_(3)………………..x_(infty) . Is equal to

If x_(n)=cospi/3^(n)+isin(pi)/(3^(n)) , then x_(1),x_(2),x_(3),………………..x_(infty) is equal to

If w=cos""(pi)/(n)+isin""(pi)/(n) then value of 1+w+w^(2)+.......+w^(n-1) is :

cos^(-1)((1-x^(2n))/(1+x^(2n)))

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 t a n x+tan(x+pi/3)+tan(x+(2pi)/3)=3, then prove that (3tanx-t a n^3x)/(1-3t a n^2x)=1 .

If f(x) is given by f(x)=(cosx+i sinx)(cos3x+isin3x) ......... ....... [cos(2n-1)x+isin(2n-1)x] , then f''(x) is equal to

If 0 lt x lt pi/2 and sin^(n) x + cos^(n) x ge 1 , then

Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^2x

If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+C_(3).x^(3)+......+C_(n).x^(n), then prove that C_(0)+2C_(1)+4C_(2)+6C_(3)+...+2n.C_(n)=1+n*2^(n)