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

If sin2 alpha=4sin2 beta, show that 5tan(alpha+beta)=3tan(alpha+beta)

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

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

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

If tan alpha=x+1,tan beta=x-1, show that 2cot(alpha-beta)=x^(2)