If `alpha,beta, in (0,pi/2) and alpha+beta=sigma` (constant) then

If 0

If alpha,beta in (0, pi/2), sinalpha=4/5 and cos(alpha+beta)=12/13 then sin beta=

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) where alpha,beta in[0,(pi)/(2)], then tan(alpha+2 beta)tan(2 alpha+beta) is equal to

If alpha,beta in(-(pi)/(2),0) such that (sin alpha+sin beta)+(sin alpha)/(sin beta)=0 and (sin alpha+sin beta)(sin alpha)/(sin beta)=-1 and lambda=lim_(n rarr oo)(1+(2sin alpha)^(2n))/((2sin beta)^(2n))

If alpha+beta=(pi)/(2) and beta+gamma=alpha then tan alpha=