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)`

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

Prove that: tan(alpha-beta)+tan(beta-gamma)+tan (gamma-alpha) = tan(alpha-beta) tan (beta-gamma) tan (gamma-alpha) .

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)

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

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 are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

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

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