Chapter 5.1, Problem 19E

To determine

To match: The given trigonometric expression with its simplest form, from the given options.

Answer to Problem 19E

The simplest form of the expression $\sec x\cos x$ is option (d) $1$ .

Explanation of Solution

Given information:

The given trigonometric expression:

  $\sec x\cos x$

The given options:

  $\sec x$ (b) $-1$ (c) $\cot x$ (d) $1$ (e) $-\tan x$ (f) $\sin x$

As per problem,

The given trigonometric expression:

  $\sec x\cos x$

Use the identity $\cos x=\frac{1}{\sec x}$ , to write the expression in terms of the secant.

  $\begin{array}{l}\sec x\cos x=\sec x(\frac{1}{\sec x})\text{}\text{}\text{}\text{ [reciprocal indentity]}\\ \text{ =1 [simplify]}\end{array}$

Hence, the simplest form of the expression $\sec x\cos x$ is option (d) $1$ .