Find the value of `x` such that `((x+alpha)^n-(x+beta)^n)/(alpha-beta)=(sin (ntheta))/(sin^n theta)`, where `alpha` and `beta` are the roots of the equation `t^2-2t+2=0`.

Find the equation whose roots are (alpha)/(beta) and (beta)/(alpha) , where alpha and beta are the roots of the equation x^(2)+2x+3=0 .

If alpha,beta are roots of the equation 3x^(2)+4x-5=0 , then (alpha)/(beta) and (beta)/(alpha) are roots of the equation

Find the sum of the series sin^2alpha+sin^2(alpha+beta)+sin^2(alpha+2beta)…+sin^2(alpha +(n-1) beta)

If alpha,beta be the roots of the equation u^2-2u+2=0 and if cottheta=x+1, then ((x+alpha)^n-(x+beta)^n)/(alpha-beta) is equal to (a) ((sin n theta),(sin^n theta)) (b) ((cosn theta),(cos^n theta)) (c) ((sinn theta),cos^n theta)) (d) ((cosn theta),(sintheta^n theta))

If sec alpha is the average of sec(alpha - 2beta) and sec(alpha + 2beta) then the value of (2 sin^2 beta - sin^2 alpha ) where beta!= n pi is

Let alpha and beta be the roots of the equation 5x^2+6x-2=0 . If S_n=alpha^n+beta^n, n=1,2,3.... then

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

If ( cos x - cos alpha)/(cos x - cos beta) = ( sin^2 alpha cos beta)/(sin^2 beta cos alpha) then cos x =

If alpha and beta are the roots of the equation 2x^(2) - 3x + 4 = 0 , then alpha^(2) + beta^(2) = ____