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, 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 alphasin(beta-gamma)+cosbetasin(gamma-alpha)+cos gammasin(alpha-beta)=

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+cosalpha+cosbeta+cosgamma=0

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

If alpha + beta = 90^@ and beta + gamma = alpha then tanalpha-tanbeta=?

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

If each of alpha, betaa n dgamma is a positive acute angle such that sin(alpha+beta-gamma) =1/2 , cos(beta+gamma-alpha)=1/2 and tan(gamma+alpha-beta)=1, find the values of alpha,betaa n dgammadot

Prove that: (tan(alpha-beta)+tan(beta-lambda)+tan(lambda-alpha) = tan(alpha-beta)tan(beta-lambda)tan(lambda-alpha)

If alpha+beta+gamma=2pi , then show that tan.alpha/2 + tan.beta/2 + tan.gamma/2 = tan.alpha/2 tan.beta/2 tan.gamma/2 .