# How will you prove the formula #cos(A-B)=cosAcosB+sinAsinB# using formula of vector product of two vectors?

##### 1 Answer

Jun 10, 2016

As below

#### Explanation:

Let us consider two **unit** vectors in X-Y plane as follows :

#hata-># inclined with positive direction of X-axis at angles**A**# hat b-># inclined with positive direction of X-axis at angles**90+B**, where# 90+B>A# - Angle between these two vectors becomes

#theta=90+B-A=90-(A-B)# ,

Now

Applying Properties of unit vectos

and

Also inserting

Finally we get