Question

Using vector algebra prove that cos(theta - phi)= cos(theta)cos(phi)-sin(theta)sin(phi) where a=cos(theta)i+sin(theta)j and b=cos(phi)+sin(phi)

Answer 1

\[a=\cos\theta\vec{i}+\sin\theta\vec{j}\\
b=\cos\phi\vec{i}+\sin\phi\vec{j}\]
You're probably familiar with the dot product. What's the dot product of a and b?