if `alpha=(-1+sqrt(-3))/2 , beta=(-1-sqrt(-3))/2` then prove that `alpha/beta+beta/alpha +1=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 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,beta and gamma are acute angled such that sin alpha = sqrt3/2 cos beta = sqrt3/2and tan gamma = 1 , then what is alpha+ beta + gamma equal to ?

If f(alpha, beta) = cos^(4)alpha/cos^(2)beta + sin^(4)alpha/sin^(2)beta then prove that f(alpha, beta) =1 ⇔ f(beta, alpha) =1 .

If alpha1=beta but alpha^(2)=2 alpha-3;beta^(2)=2 beta-3 then the equation whose roots are (alpha)/(beta) and (beta)/(alpha) is

If alpha,beta,gamma are different from 1 and are the roots of ax^(3)+bx^(2)+cx+d=0 and (beta-gamma)(gamma-alpha)(alpha-beta)=(25)/(2) ,then prove that det[[(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)alpha,beta,gammaalpha^(2),beta^(2),gamma^(2)]]=(25d)/(2(a+b+c+d))