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Chapter 2: Problem 105

In Exercises 103-108, determine whether or not the equation is an identity, and give a reason for your answer. $$ \frac{1}{(5 \cos \theta)}=5 \sec \theta $$

Short Answer

Expert verified
The given equation is not an identity.

Step by step solution

01

Understanding the Various forms of Trigonometric Functions

It is important to understand the reciprocal relationships between different trigonometric functions. In this case, the function sec 胃 is the reciprocal of cos 胃, i.e., \( \sec \theta = \frac{1}{\cos \theta} \)
02

Examine the Given Equation

The given equation is \( \frac{1}{5 \cos \theta} = 5 \sec \theta \) . Start by manipulating the right side of the equation to make it look like the left side. We know the definition of sec 胃, so rewrite the right side using this definition: \( 5 \sec \theta = 5 * (\frac{1}{\cos \theta}) \).
03

Compare Both Sides of The Equation

When simplified, the right side of the equation turns out to be \( \frac{5}{\cos \theta} \) and the left side of the equation is \( \frac{1}{5 \cos \theta} \) . Thus, they are not the same, therefore the equation is not an identity.

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