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

"Show that :" 2 sin^(2) beta + 4 cos ( alpha + beta) sin alpha sin beta + cos2 (alpha + beta) = cos2 alpha

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

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

Show that 2"sin"^(2)beta+4 cos(alpha+beta)"sin" alpha sin beta+cos2(alpha+beta)=cos 2alpha .

Simplify 2sin^(2)beta+4cos(alpha+beta)sin alpha sin 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: cos ^ (2) alpha + cos ^ (2) (alpha + beta) -2cos alpha cos beta cos (alpha + beta) = sin ^ (2) beta

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

If cos alpha+cos beta=0=sin alpha+sin beta then cos2 alpha+cos2 beta=