Show that `cos ^2 alpha + cos^2 (alpha`+Beta) - 2 cos alpha cos betacos (alpha+ beta) =sin^2 beta

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

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

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

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

If y = sin ^(2) alpha + cos ^(2) (alpha + beta) + 2 sin alpha sin betacos(alpha+beta) then (d^(3)y)/(dalpha^(3))=?

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)

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

Sum the series cosalpha+^nC_1 cos(alpha+beta)+^nC_2 cos (alpha+2beta)+…+cos(alpha+nbeta)

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