Chapter 5, Problem 1RE

Concept Check For each expression in Column I, choose the expression from Column II that completes an identity.

	II
A. $\frac{1}{\mathrm{s}\mathrm{i}\mathrm{n} x}$	B. $\frac{1}{\mathrm{c}\mathrm{o}\mathrm{s} x}$
C. $\frac{\mathrm{s}\mathrm{i}\mathrm{n} x}{\mathrm{c}\mathrm{o}\mathrm{s} x}$	D. $\mathit{ }\frac{1}{{\mathrm{c}\mathrm{o}\mathrm{t}}^2 x}$
E. $\frac{1}{{\mathrm{c}\mathrm{o}\mathrm{s}}^2 x}$	F. $\frac{\mathrm{c}\mathrm{o}\mathrm{s} x}{\mathrm{s}\mathrm{i}\mathrm{n} x}$

sec x= ___________

To determine

To calculate: The exact value in the column II with the expression $\sec x$.

Answer to Problem 1RE

Solution: $\underset{\_}{\text{B}}$

Explanation of Solution

Given: $\sec x$

The options are

$\begin{array}{cc}& \text{Column II}\\ \text{A}\text{.}& \frac{1}{\sin x}\\ \text{B}\text{.}& \frac{1}{\cos x}\\ \text{C}\text{.}& \frac{\sin x}{\cos x}\\ \text{D}\text{.}& \frac{1}{{\cot }^{2}x}\\ \text{E}\text{.}& \frac{1}{{\cos }^{2}x}\\ \text{F}\text{.}& \frac{\cos x}{\sin x}\end{array}$

Formula used: The reciprocal identity of secant function which is defined as:

$\sec A=\frac{1}{\cos A}$

Calculation: Applying the above formula on the provided expression is:

$\sec x=\frac{1}{\cos x}$

Therefore, the correct match of the provided expression will be $\left(\text{B}\text{.}\right)\frac{1}{\cos x}$.