Prove that for any vector A and B the following is true

Question

llAxBll^2 +lA·Bl^2 =llAll^2 llBll^2

Answer 1

A×B = |A|*|B|*sinθ
A•B = |A|*|B|*cosθ
now, what is your most basic trig identity?

Answer 2

vector identity :
|A×B| = |A|*|B|*sinθ