Simplify (sin(theta)^3cos(theta))/(cos(theta)^4)

$\frac{\sin^{3} (θ) \cos (θ)}{\cos^{4} (θ)}$

Cancel the common factor of $\cos (θ)$ and $\cos^{4} (θ)$ .

Factor $\cos (θ)$ out of $\sin^{3} (θ) \cos (θ)$ .

$\frac{\cos (θ) \sin^{3} (θ)}{\cos^{4} (θ)}$

Cancel the common factors.

Factor $\cos (θ)$ out of $\cos^{4} (θ)$ .

$\frac{\cos (θ) \sin^{3} (θ)}{\cos (θ) \cos^{3} (θ)}$

Cancel the common factor.

$\frac{\cos (θ) \sin^{3} (θ)}{\cos (θ) \cos^{3} (θ)}$

Rewrite the expression.

$\frac{\sin^{3} (θ)}{\cos^{3} (θ)}$

Convert from $\frac{\sin^{3} (θ)}{\cos^{3} (θ)}$ to $\tan^{3} (θ)$ .

$\tan^{3} (θ)$