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 cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

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

Prove that |cos alpha-cos beta|<=| alpha-beta|

If cos alpha+cos beta=0=sin alpha+sin beta. Prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos(alpha-beta)+1=0, show that cos alpha+cos beta=0 and sin alpha+sin beta=0

If alpha + beta + gamma = 2 theta , prove that cos theta + cos(theta- alpha) + cos(theta- beta) + cos(theta -gamma) = 4(cos (alpha/2) cos (beta/2) cos (gamma/2))

If cos alpha+cos beta+cos gamma=0, then prove that cos3 alpha+cos3 beta+cos3 gamma=12cos alpha cos beta cos gamma

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