If `cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2`,show that `cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0`

If alpha+beta=gamma ,show that cos^2alpha+cos^2beta+cos^2gamma=1+2cosalphacosbetacosgamma

If secalpha+secbeta+secgamma=0 ,show that (cosalpha+cosbeta+cosgamma)^2=cos^2alpha+cos^2beta+cos^2gamma

If alpha+beta+gamma=0 ,prove that cosalpha+cosbeta+cosgamma=4cos(alpha/2)cos(beta/2)cos(gamma/2)-1

If cos^2alpha-sin^2alpha=tan^2beta ,show that cos^2beta-sin^2beta=tan^2alpha

Prove that (cos alpha-cos beta)^2+(sin alpha-sin beta)^2=4sin^2((alpha-beta)/2)

If tanbeta=(nsinalphacosalpha)/(1-nsin^2alpha) ,show that tan(alpha-beta)=(1-n)tanalpha

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4 cos((alpha+beta)/2)cos((beta+gamma)/2)cos((gamma+alpha)/2)

If alpha and beta be two acute angles and cos2alpha=(3cos2beta-1)/(3-cos2beta) ,show that tan alpha=sqrt2tanbeta

Prove that |(alpha, beta, gamma),(alpha^(2), beta^(2), gamma^(2)),(beta+gamma , gamma + alpha, alpha + beta)| = (alpha-beta)(beta-gamma)(gamma-alpha)(alpha + beta + gamma) .