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

What is sin (alpha+beta) - 2 sin alpha cos beta + sin(alpha- beta) =

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

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)

(sinalpha cos beta+cos alpha sin beta)^2+(cos alpha cos beta-sin alpha sin beta)^2=1

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

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

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