If `cosalpha=1/(sqrt(2)),sinbeta=1/(sqrt(3))` , show that `tan((alpha+beta)/2)cot((alpha-beta)/2)=5+2sqrt6` or `5-2sqrt6`

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 cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 ,show that tan ((alpha+beta)/2)=3/4

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

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

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

If sin beta = 1/5 sin(2alpha +beta) , show that tan(alpha +beta) = 3/2 tan alpha .

If sinalpha-sinbeta=1/3andcosbeta-cosalpha=1/2, show that cot(alpha+beta)/2=2/3

If sinalpha-sinbeta=1/3andcosbeta-cosalpha=1/2, show that cot(alpha+beta)/2=2/3

tan_(tan6 beta)(alpha+beta)=sqrt(3),tan(alpha-beta)=1 then