If `alpha+beta= 60^0`, prove that `cos^2 alpha + cos^2 beta - cosalpha cos beta = 3/4`.

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

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

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha+cos2beta+2cos(alpha+beta)=0

If cosalpha+cosbeta=0=s inalpha+s inbeta, then prove that cos2alpha+cos2beta=-2cos(alpha+beta)dot

Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta

If 2 tan (alpha/2)=tan (beta/2), prove that cos alpha=(3+5 cos beta)/(5+3 cos beta).

If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, alpha beta in [0, pi] , then cos (alpha + beta) - cos (alpha - beta) is equal to -sqrt(k) . The value of k is _________.

lf cos^2 alpha -sin^2 alpha = tan^2 beta , then show that tan^2 alpha = cos^2 beta-sin^2 beta .

A line makes angles alpha,beta,gamma and delta with the diagonals of a cube, prove that cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4/3