If `x=a+b,y=a gamma+b beta and z=abeta+ b gamma` , where `gamma and beta` are the imaginary cube roots ofunity, then `xyz=`

If alpha < beta < gamma and sin gamma cos alpha=1, where alpha,gamma in[pi,2 pi], then the least integral value of f(x) = | x - alpha| + | x - beta| + |x - gamma| is

If alpha,beta,gamma are the roots of a x^3+b x^2+c x+d=0a n d|alpha beta gamma beta gamma alpha gamma alpha beta|=0,alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha,a n dgamma+alpha-betadot

IF alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

A circle x^(2)+y^(2)=a^(2) meets the x-axis at A(-a,0) and B(a,0). P(alpha) and Q( beta ) are two points on the circle so that alpha-beta=2 gamma, where gamma is a constant. Find the locus of the point of intersection of AP and BQ.

If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2 alpha + 2 tan^2 alpha tan^2 beta tan^2 gamma = 1 then sin^2 alpha + sin^2 beta + sin^2 gamma =

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

Let alpha ,beta and gamma be the roots of the equations x^(3) +ax^(2)+bx+ c=0,(a ne 0) . If the system of equations alphax + betay+gammaz=0 beta x +gamma y+ alphaz =0 and gamma x =alpha y + betaz =0 has non-trivial solution then

If tan beta=2sin alpha sin gamma co sec(alpha+gamma) , then cot alpha,cot beta,cotgamma are in