Work each exercise. Show that sec(-x)=secx by writing sec(-x) as (1)/(cos(-x)) and then using th

step 1 we are going to do problem number 31 in this question we are going to prove sake x is equal to s

Work each exercise. Show that sec(-x)=secx by writing...

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Key Concepts

Reciprocal Trigonometric Functions

This concept involves understanding that some trigonometric functions are defined as the reciprocal of another function. For example, the secant function is defined as the reciprocal of the cosine function, which is written as sec(x) = 1/cos(x). Recognizing these relationships is essential when proving trigonometric identities.

Even Functions in Trigonometry

An even function is a function that satisfies the condition f(-x) = f(x) for every value of x in its domain. In trigonometry, the cosine function is a prime example of an even function, meaning that cos(-x) = cos(x). This property is crucial when extending results from cosine to other functions defined in terms of cosine, such as secant.

Trigonometric Identities

Trigonometric identities are equations that hold true for all values of the variables involved. They are used to simplify expressions and prove relationships between different trigonometric functions. In this context, the identity cos(-x) = cos(x) is applied to demonstrate that sec(-x) equals sec(x) by substituting and simplifying the reciprocal relationship.

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