Proving angle sum trig identies w/ vector and scalar products

[bossman007]

Homework Statement

I need to prove both of these (in exercise 11)

[PLAIN]http://postimage.org/image/x7shxv11f/ [/PLAIN]

Homework Equations

The dot product

The Attempt at a Solution

 

[clamtrox]

What do you mean where did you go wrong? Isn't that what you were asked to prove? You really need to write down some intermediate steps though. It's impossible to follow your "proof" as it is now. Now you just wrote down the starting point and the end result.

 

[vela]

Your first mistake is in the very first line: What is $\vec{A}\vec{B}\cos(\theta+\phi)$ supposed to mean? You can't just stick two vectors next to each other like that. $\vec{A}\cdot\vec{B}$ makes sense because it's saying your dotting the two vectors together; similarly, $\vec{A}\times\vec{B}$ makes sense because it's saying you're taking the cross product. $\vec{A}\vec{B}$ doesn't mean anything.

Your second mistake is that you're using the very identity you're trying to prove. So far, you're using the fact that $\vec{A}\cdot\vec{B} = |\vec{A}||\vec{B}|\cos(\theta+\phi)$. You need to find a second way to express the dot product.