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

If alpha + beta+gamma=pi , prove that sin^2 alpha + sin^ beta - sin^2 gamma = 2sinalpha sinbeta cosgamma

If 0ltalphalt pi/2, 0ltbetaltpi/2 and 0ltgammalt pi/2 prove that sin(alpha+beta+gamma) lt sinalpha+sinbeta +sin gamma

If alpha+beta+gamma=2pi then

Given alpha+beta-gamma=pi, prove that sin^(2)alpha+sin^(2)beta-sin^(2)gamma=2sin alpha sin beta cos gamma

Given alpha+beta-gamma=pi, prove that sin^(2)alpha+sin^(2)beta-sin^(2)gamma=2sin alpha sin beta cos gamma

If alpha + beta- gamma= pi , prove that sin^(2)alpha + sin^(2)beta - sin^(2)gamma = 2sin alpha sin beta cos gamma .

cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-(3)/(2), prove that cos alpha+cos beta+cos gamma=sin alpha+sin beta+sin gamma=0

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

If sinalpha+sinbeta+singamma=cosalpha+cosbeta+cosgamma=0 then prove that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

Let alpha,beta,gamma>0 and alpha+beta+gamma=(pi)/(2). Then prove that sqrt(tan alpha tan beta)+sqrt(tan beta tan gamma)+sqrt(tan alpha tan gamma)<=sqrt(3)