Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 201: 43

$$\cos^2 x=\frac{1}{\sec^2 x}$$ $\text{B}$ is the answer.

$$A=\cos^2 x$$ According to this Reciprocal Identity: $$\sec\theta=\frac{1}{\cos\theta}$$ $$\cos\theta=\frac{1}{\sec\theta}$$ Therefore, $A$ can be rewritten as follows: $$A=\frac{1}{\sec^2 x}$$ $\text{B}$ is the answer.