Math Snap

STEP 1

1. The expression involves trigonometric identities.
2. The goal is to simplify the expression to a single sine or cosine function.
3. We will use angle sum identities to achieve this.

STEP 2

1. Recognize the expression as a form that can be simplified using angle sum identities.
2. Apply the angle sum identity for sine.

STEP 3

Recognize that the expression $\cos 4\theta \sin \theta - \sin 4\theta \cos \theta$ can be written in the form of a sine angle sum identity:
The sine angle sum identity is:
$$\sin(A - B) = \sin A \cos B - \cos A \sin B$$ In this expression, let $A = 4\theta$ and $B = \theta$.

STEP 4

Apply the sine angle sum identity:
$$\cos 4\theta \sin \theta - \sin 4\theta \cos \theta = \sin(4\theta - \theta)$$

Simplify the expression inside the sine function:
$$4\theta - \theta = 3\theta$$ Thus, the expression simplifies to:
$$\sin(3\theta)$$ The expression $\cos 4\theta \sin \theta - \sin 4\theta \cos \theta$ is equivalent to:
$$\sin(3\theta)$$