If `alpha+beta+gamma=pi` and `tan((beta+gamma-alpha)/4)tan((gamma+alpha-beta)/4)tan((alpha+beta-gamma)/4)=1`. Prove that `1+cosalpha+cosbeta+cosgamma=0`

If alpha+beta+gamma=pi and tan((beta+gamma-alpha)/(4))tan((gamma+alpha-beta)/(4))tan((alpha+beta-gamma)/(4))=1. Prove that 1+cos alpha+cos beta+cos gamma=0

If alpha + beta + gamma = pi , show that : tan (beta+gamma-alpha) + tan (gamma+alpha-beta) + tan (alpha+beta-gamma) = tan (beta+gamma-alpha) tan (gamma+alpha-beta) tan (alpha+beta-gamma)

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

sin (beta+ gamma- alpha) + sin (gamma+ alpha - beta) + sin (alpha + beta- gamma)- sin (alpha + beta + gamma)=

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

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