Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 497: 37

The left side of the equation is equivalent to $\cos{x}-\sin^2{x}\cos{x}$ therefore the given equation is an identity. Refer to the solution below.

\begin{align} \text{LHS } &= \cos^3{\theta} \\[2mm] &= \cos{x} \cdot \cos^2{x} \\[2mm] &= \cos{x} (1-\sin^2{x}) \\[2mm] &= \cos{x}-\sin^2{x} \cos{x} \\[2mm] &= \text{ RHS} \end{align}