[sin^(2)alpha+cos^(2)(alpha+beta)+2sin alpha sin beta cos(alpha+beta)=],[" 1) "sin^(2)alpha" 2) "sin^(2)beta" 3) "cos^(2)alpha" 4) "cos^(2)beta]

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

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

sin ^ (2) alpha + cos ^ (2) (alpha + beta) + 2 sin alpha sin beta cos (alpha + beta) = (i) sin ^ (2) (alpha) (ii) sin ^ (2) (beta ) (iii) cos ^ (2) (alpha) (iv) cos ^ (2) (beta)

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

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

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

If cos(alpha+beta)=0 then sin^(2)alpha+sin^(2)beta