if `alpha=(-1+sqrt(-3))/2 , beta=(-1-sqrt(-3))/2` then prove that `alpha/beta+beta/alpha +1=0`

If alpha=(-1-sqrt-3)/(2) and beta=(-1+sqrt(-3))/(2), "show that" alpha^(2)+alphabeta+beta^(2)=0.

If sin alpha=(1)/(sqrt(10)) and sin beta=(1)/(sqrt(5)) then prove that alpha+beta=(pi)/(4)

If cos alpha=(1)/(sqrt(2)),sin beta=(1)/(sqrt(3)), show that tan((alpha+beta)/(2))cot((alpha-beta)/(2))=5+2sqrt(6) or 5-2sqrt(6)

If alpha=tan^(-1)((sqrt(3)x)/(2y-x)),beta=tan^(-1)((2x-y)/(sqrt(3y)))" then "alpha-beta=

If tan alpha=(1)/(7),sin beta=(1)/(sqrt(10)), prove that alpha+2 beta=(pi)/(4), where 0

If tan alpha=(1)/(7),sin beta=(1)/(sqrt(10)), Prove that :alpha+2 beta=(pi)/(4), where 0

If tan alpha = sqrt(3) and tan beta = (1)/(sqrt(3)) , then find the value of cot (alpha + beta) .

If sin alpha=(3)/(sqrt(73)),cos beta=(11)/(sqrt(146)) where alpha,beta in[0,(pi)/(2)] then (alpha+beta) is equal to-

If alpha and beta are positive acute angles and cos2alpha=(3cos2beta-1)/(3-cos2beta) ,then prove that tan alpha=sqrt2tanbeta