How will you prove the formula #sin(A+B)=sinAcosB+cosAsinB# using formula of scalar product of two vectors?
both unit vectors, because
Have their inner product given by
This is exactly
If we take complex numbers and using the de Moivre's identity which reads
In the case of vectors we have projections and in the case of complex numbers we have rotations.
Using vectors with additional phase additions we can obtain also
It is left as an exercise.