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

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

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

Prove that sin^(2)alpha+cos^(2)(alpha+beta)+2sinalphasinbetacos(alpha+beta) is independent of alpha .

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

If A = cos ^(2) alpha + cos ^2(alpha + beta)- 2 cos alpha cos beta cos (alpha + beta), then

underset is f(alpha. beta)=cos^(2)+beta cos^(2)(alpha+beta)-2cos alpha cos beta cos(alpha+beta)

Prove that cos^(2)(alpha-beta)+cos^(2)beta-2cos(alpha-beta)cosalphacosbeta is independent of beta .

Prove that: cos2 alpha cos2 beta+sin^(2)(alpha-beta)-sin^(2)(alpha+beta)=cos2(alpha+beta)

Prove that sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin beta cos (alpha + beta) is independent of alpha .

Prove that 2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=cos2 alpha