Let `alpha,beta,gamma>0a n dalpha+beta+gamma=pi/2dot` Then prove that `sqrt(tanalphatanbeta)` + `sqrt(t a nbeta"tan"gamma)+sqrt(tanalphatangamma)lt=sqrt(3)`

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

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)

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

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

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 alpha+beta+gamma=2pi, then (a) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=tan(alpha/2)tan(beta/2)tan(gamma/2) (b) tan(alpha/2)tan(beta/2)+tan(beta/2)tan(gamma/2)+tan(gamma/2)tan(alpha/2)=1 (c) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=-tan(alpha/2)tan(beta/2)tan(gamma/2) (d)none of these

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

If tanalpha=1/7,sin beta=1/(sqrt(10)), prove that alpha+2beta=pi/4

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

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 .