Angle sum and difference identities can make math a lot easier when you're working with trigonometry. Here’s how they help:

1. Breaking Down Complex Angles: Instead of trying to figure out something like $\sin(75^\circ)$ right away, you can think of it as $\sin(45^\circ + 30^\circ)$. This splits it into simpler pieces:

   $$\sin(75^\circ) = \sin(45^\circ)\cos(30^\circ) + \cos(45^\circ)\sin(30^\circ$$

2. Avoiding the Calculator: Sometimes, you need to find the sine or cosine for angles that don’t fit perfectly into your unit circle. These identities allow you to express them using angles that you already know.

3. Easier Problem-Solving: They also help when you are trying to prove things about triangles or when you're solving trig equations more easily.

In short, using these identities makes pre-calculus much simpler!