For each expression in Column I, choose the expression from Column II that completes an identity.
6. sec² x = ____

Key Concepts

Secant Function

The secant function, denoted as sec(x), is the reciprocal of the cosine function. It is defined as sec(x) = 1/cos(x). Understanding secant is crucial for solving trigonometric identities, as it relates directly to the cosine function and can be expressed in terms of sine and cosine.

Pythagorean Identity

Pythagorean identities are fundamental relationships in trigonometry that involve the squares of sine, cosine, and tangent functions. The most common identity is sin²(x) + cos²(x) = 1. This identity can be manipulated to express sec²(x) in terms of tangent, specifically sec²(x) = 1 + tan²(x), which is essential for completing the given expression.

Trigonometric Identities

Trigonometric identities are equations that hold true for all values of the variables involved. They are used to simplify expressions and solve equations in trigonometry. Recognizing and applying these identities, such as the relationship between secant and tangent, is key to completing the expression in the question accurately.