`("lim")_(xvecoo)"{"(n/(n+1))^(alpha)+s in1/n]^n`(when `alpha in Q`) is equal to (a) `e^(-alpha)` (b) `-alpha` (c) `e^(1-alpha)` (d) `e^(1+alpha)`

lim_ (n rarr oo) (n ^ (alpha) sin ^ (2) n!) / (n + 1), 0

The product prod_(r=1)^(2n-1)tan(r alpha)( where 4n alpha=pi) is equal to

if cos^(2)alpha-sin alpha=(1)/(n) then alpha

cos (n + 1) alpha cos (n-1) alpha + sin (n + 1) alpha sin (n-1) alpha =

If alpha=e^((i2 pi)/(n)), then n(11-alpha)(11-alpha^(2))(11-alpha^(n-1))=

If alpha is the nth root of unity,then 1+2 alpha+3 alpha^(2)+rarr n terms equal to a.(-n)/((1-alpha)^(2)) b.(-n)/(1-alpha^(2)) c.(-2n)/(1-alpha) d.(-2n)/((1-alpha)^(2))

If 1,alpha_1, alpha_2, …alpha_(n-1) be n, nth roots of unity show that (1-alpha_1)(1-alpha_2).(1-alpha(n-1)=m

(1)/(cos alpha+cos3 alpha)+(1)/(cos alpha+cos5 alpha)...(.1)/(cos alpha+cos(2n+1)alpha)