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

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

If alpha=^m C_2,t h e n^(alpha)C_2 is equal to

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

If n=pi/(4alpha), then tanalpha tan 2alpha tan 3 alpha........tan(2n-1)alpha is equal to

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

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

If alpha_(1), alpha_(2), alpha_(3), alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 , then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4)) is

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))