If `alpha_(1), alpha_(2), alpha_(3), beta_(1), beta_(2), beta_(3)` are the values of n for which `sum_(r=0)^(n-1)x^(2r)` is divisible by `sum_(r=0)^(n-1)x^(r )`, then the triangle having vertices `(alpha_(1), beta_(1)),(alpha_(2),beta_(2))` and `(alpha_(3), beta_(3))` cannot be

If Delta = |(cos (alpha_(1) - beta_(1)),cos (alpha_(1) - beta_(2)),cos (alpha_(1) - beta_(3))),(cos (alpha_(2) - beta_(1)),cos (alpha_(2) - beta_(2)),cos (alpha_(2) - beta_(3))),(cos (alpha_(3) - beta_(1)),cos (alpha_(3) - beta_(2)),cos (alpha_(3) - beta_(3)))|" then " Delta equals

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 alpha and beta be the roots of the equation x^(2)-2x+2=0 , then the least value of n for which ((alpha)/(beta))^(n)=1 is:

alpha and beta are acute angles and cos2alpha = (3cos2beta-1)/(3-cos2beta) then tan alpha cot beta =

The lengths of the sides of a triangle are alpha-beta, alpha+beta and sqrt(3alpha^2+beta^2), (alpha>beta>0) . Its largest angle is

Sum the series tan alpha tan (alpha+beta)+tan(alpha+beta)+tan(alpha+2beta)+tan(alpha+2beta)tan(alpha+3beta)+… to n terms

If alpha , beta , gamma are the roots of x^3 +qx +r=0 then sum ( beta + gamma )^(-1) =

Let log_(3)N=alpha_(1)+beta_(1) log_(5)N=alpha_(2)+beta_(2) log_(7)N=alpha_(3)+beta_(3) where alpha_(1), alpha_(2) and alpha_(3) are integers and beta_(1), beta_(2), beta_(3) in [0,1) . Q. Difference of largest and smallest values of N if alpha_(1)=5, alpha_(2)=3 and alpha_(3)=2 .

If alpha , beta , gamma are the roots of x^3 +px^2 +qx +r=0 then find sum (1)/( alpha )