Determine the values of `alpha, beta, gamma` when `[{:(0,2sinbeta,tan gamma),(cos alpha, sin beta,-tan gamma),(cos alpha, -sin beta, tan gamma):}]` is orthogonal.

Determine the values of alpha ,beta , gamma when [{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}] is orthogonal.

If sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 gamma=

If cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma , then (sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma)) is equal to

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

If a right angle be divided into three parts alpha, beta and gamma , prove that cot alpha = (tan beta + tan gamma)/(1-tan beta tan gamma) .

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

Evaluate the following: |[1,1,1],[alpha, beta, gamma],[beta gamma, gamma alpha, alpha beta]|

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

The expression cos^(2)(alpha + beta + gamma) + cos^(2)(beta + gamma) + cos^(2)alpha - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma) is (a) independent of alpha (b) independent of beta (c) dependent on gamma only (d) dependent on alpha, beta, gamma

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