The angle between two vectors non-zero is defined by the equation

The inequality

we established in the previous exercise (Section 12.17, Exercise #6) show that there is a unique satisfying this equation. Prove that we have

*Proof.* From the definition of we have

But then we know from this exercise (Section 12.17, Exercise #3) that

And, we know from this exercise (Section 12.17, Exercise #5) that

Therefore,