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

If alpha+beta-gamma=pi and sin^2alpha+sin^2beta-sin^2gamma=lambda sinalpha sinbeta cosgamma, then write the value of lambda

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+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 sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 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=0=sin alpha+sin beta+sin gamma , then (sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma)) is equal to

If a line makes anles alpha, beta, gamma with the coordinate axes, porve that sin^2alpha+sin^2beta+sin^2gamma=2

If alpha, beta, gamma are the angles which a line makes with the coordinate axes ,then (A) sin^2alpha=cos^2beta+cos^2gamma (B) cos^2alpha+cos^2beta+cos^2gamma=2 (C) cos^2alpha+cos^2beta+cos^2gamma=1 (D) sin^2alpha+sin^2beta=1+cos^2gamma

Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=cos2(alpha+beta) .

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