If `U_n=int_0^pi(1-cosnx)/(1-cosx)dx ,` where `n` is positive integer or zero, then show that `U_(n+2)+U_n=2U_(n+1)dot` Hence, deduce that `int_0^(pi/2)(sin^2ntheta)/(sin^2theta)=1/2npidot`

If U_(n)=int_(0)^( pi)(1-cos nx)/(1-cos x)dx, where n is positive integer or zero,then show that U_(n+2)+U_(n)=2U_(n+1). Hence,deduce that int_(0)^((pi)/(2))(sin^(2)n theta)/(sin^(2)theta)=(1)/(2)n pi

If U_(n)=int_(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of zero, then The value of U_(n) is

If U_(n)=int_(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of zero, then The value of U_(n) is a. pi//2 b. pi c. npi//2 d. npi

If U_(n)=int_(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of zero, then The value of int_(0)^(pi//2)(sin^(2)n theta)/(sin^(2) theta) d theta is

L e tf(n)=1+1/2+1/3++1/ndot Then show that f(n)=int_0^(pi/2)cot(theta/2)(1-cos^ntheta)d theta

If u_(n)=2Cos^(n) theta then show that u_(1)u_(n)-u_(n-1)= u_(n+1)

If U_n=int_0^(pi/2)(sin^2n x)/(sin^2x)dx, then show that U_1,U_2,U_3.......U_n constitute an AP. Hence or otherwise find the value of U_n.

If U_n=int_0^(pi/2)(sin^2n x)/(sin^2x)dx, then show that U_1,U_2,U_3.......U_n constitute an AP. Hence or otherwise find the value of U_n.

If n is a positive integer, prove that: int_0^(2pi) (cos(n-1)x-cosnx)/(1-cosx)dx=2pi , hence or otherwise, show that int_0^(2pi) (sin((nx)/2)/sin(x/2))^2dx=2npi .