Chapter 7.1, Problem 5E

To determine

To simplify the given expression.

Answer to Problem 5E

  $\sin \theta \sec \theta =\tan \theta$

Explanation of Solution

Given:

An expression is given as

  $\sin \theta \sec \theta$

Concept Used:

The trigonometric identities:

$\begin{array}{l}\sec x=\frac{1}{\cos x}\\ \tan x=\frac{\sin x}{\cos x}\end{array}$

Calculation:

In order to simplify the expression:

  $\sin \theta \sec \theta$

Now, simplify the given expression as shown:

  $\begin{array}{c}\sin \theta \sec \theta =\sin \theta \times \frac{1}{\cos \theta }\\ =\frac{\sin \theta }{\cos \theta }\\ =\tan \theta \end{array}$

Thus, the simplified form of the expression is

  $\sin \theta \sec \theta =\tan \theta$