Math Snap

STEP 1

1. We assume the basic trigonometric identities are known: $\tan \theta = \frac{\sin \theta}{\cos \theta}$.
2. We assume the domain of $\theta$ is such that $\cos \theta \neq 0$.

STEP 2

1. Express $\tan \theta$ in terms of $\sin \theta$ and $\cos \theta$.
2. Substitute the expression for $\tan \theta$ into the left-hand side of the identity.
3. Simplify the expression to show it equals the right-hand side.

STEP 3

Start by expressing $\tan \theta$ in terms of $\sin \theta$ and $\cos \theta$:
$$\tan \theta = \frac{\sin \theta}{\cos \theta}$$

STEP 4

Substitute the expression for $\tan \theta$ into the left-hand side of the identity $\cos \theta \times \tan \theta$:
$$\cos \theta \times \tan \theta = \cos \theta \times \frac{\sin \theta}{\cos \theta}$$

Simplify the expression by canceling $\cos \theta$ in the numerator and the denominator:
$$\cos \theta \times \frac{\sin \theta}{\cos \theta} = \sin \theta$$ The identity is proven:
$$\cos \theta \times \tan \theta = \sin \theta$$