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

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

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

Prove that cos 4A=1-8cos^2A+8 cos^4A

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

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) .

if xcosalpha+ysinalpha=k=xcosbeta+ysinbeta ,show that x/(cos((alpha+beta)/2))=y/(sin((alpha+beta)/2))=k/(cos((alpha-beta)/2))

Prove that in case of expansion of solid beta = 2alpha .

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