Given `alpha+beta-gamma=pi,` prove that `sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot`

If cosalpha+cosbeta+cosgamma=0a n da l sosinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

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

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that sin 3alpha + sin 3 beta + sin 3gamma = 3 sin (alpha + beta + gamma)

If tanbeta=(tanalpha+tangamma)/(1+tanalphatangamma)dot prove that sin2beta=(sin2alpha+sin2gamma)/(1+sin2alphasin2gamma) .

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

If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 , then the value of sin3alpha+8sin3beta+27sin3gamma is a. sin(alpha+beta+gamma) b. 3sin(alpha+beta+gamma) c. 18"sin"(alpha+beta+gamma) d. sin(alpha+2beta+3)

If alpha,beta,gamma are the direction angles of a line (i)Show that sin^2 alpha + sin^2 beta +sin^2 gamma=2 . (ii)Find the value of cos2alpha +cos2beta+cos2gamma .

If (cos^(4)alpha)/(cos^(2) beta) + (sin^(4)alpha)/(sin^(2)beta) = 1, prove that sin^(4)alpha + sin^(4) beta = 2 sin^(2) alpha sin^(2) beta

If cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y+1/y),(x y >0); x , y ,alpha,beta in R then sin(alpha+beta+gamma+singammaAAgamma in R cosalphacosbeta=1AAalpha,beta in R (cosalpha+cosbeta)^2=4AAalpha,beta in R sin(alpha+beta+gamma)=sinalpha+sinbeta+s ingammaAAa , b ,gamma in R

Prove that sum_(alpha+beta+gamma = 10) (10 !)/(alpha!beta!gamma!)=3^(10)dot