Prove by vector method that `cos(A+B)cos AcosB-sinAsinBdot`

Explanation

Let `hati and hatj` be unit vectors along OX and OY, respectively.
Let `vecOP.vecOQ` be two unit vectors drawn in the plane XOY such that.
`angleXOP=A , angleXOQ= B`
POQ= A+B
now `vecOP = hati cos A+hatj sin A`
`vecOQ=hati cos B + hatj sin B`
`vecOP.vecOQ= cosA cosB-sinA sinB`
`(1) (1) cos (A+B)=cosA cosB -sin B - sin A sinB`
`cos (A+B) = cos AcosB-sinA sinB`