If `alpha+beta=pi/2a n dbeta+gamma=alpha,` then `tanalpha` equals

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

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 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma are in

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)

If cos^(-1) alpha + cos^(-1) beta + cos^(-1) gamma = 3pi , then alpha (beta + gamma) + beta(gamma + alpha) + gamma(alpha + beta) equal to

If alpha < beta < gamma and sin gamma cos alpha=1, where alpha,gamma in[pi,2 pi], then the least integral value of f(x) = | x - alpha| + | x - beta| + |x - gamma| is

If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha , and gamma+alpha-beta .

If alpha, beta, gamma are the roots of the equation x^3 + px^2 + qx + r = n then the value of (alpha - 1/(beta gamma)) (beta -1/(gamma alpha)) (gamma-1/(alpha beta)) is:

If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0 , then the value of |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| , is