Prove by vector methods that `sin(alpha+beta)=sin alphacos beta+cos alphasin beta`

Prove by vector method that sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta.

By vector method, Prove that sin(alpha-beta)=sinalphacosbeta-cosalphasinbeta

Prove by vectors that : cos (alpha + beta) = cos alpha cos beta- sin alpha sin beta .

Prove by vectors that : cos (alpha - beta) = cos alpha cos beta+ sin alpha sin beta .

Using vectors prove that sin(alpha - beta) = sin alpha cos beta- cos alpha sin beta .

Using vectors, prove that sin (alpha+beta)=sin alpha cos beta+ cos alpha sin beta .

(i) sin (alpha + beta) = sin alpha cos beta + cos alpha sin beta) (ii) sin (alpha-beta)= sin alpha cos beta- cos alpha sin beta Proof

Prove the following identities: (cos alpha cos beta+sin alphasin beta)^2+(sinalphacos beta-cos alphasinbeta)^2=1

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