In Exercises 127–130, solve each equation on the interval [0, 2𝝅) by first rewriting the equation in terms of sines or cosines.sec² x + 3 sec x + 2 = 0

The secant function, denoted as sec(x), is the reciprocal of the cosine function, defined as sec(x) = 1/cos(x). It is important to understand how secant relates to cosine, as this relationship allows us to rewrite equations involving secant in terms of cosine or sine, facilitating easier manipulation and solving.

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. Key identities include the Pythagorean identities, reciprocal identities, and co-function identities. These identities are essential for rewriting and simplifying trigonometric equations, such as converting secant functions into sine and cosine functions.

Interval notation is a mathematical notation used to represent a range of values. In this context, the interval [0, 2π) indicates that the solutions to the equation should be found within the range starting from 0 (inclusive) to 2π (exclusive). Understanding interval notation is crucial for determining the valid solutions of trigonometric equations within specified bounds.