# How will you prove the formula #sin(A+B)=sinAcosB+cosAsinB# using formula of scalar product of two vectors?

##### 1 Answer

See below.

#### Explanation:

Given

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.