Match each expression in Column I with its value in Column II.
cos² (π/6) - sin² (π/6)

Key Concepts

Trigonometric Functions

Trigonometric functions, such as sine and cosine, relate the angles of a triangle to the lengths of its sides. For example, cos(θ) gives the ratio of the adjacent side to the hypotenuse, while sin(θ) gives the ratio of the opposite side to the hypotenuse. Understanding these functions is essential for evaluating expressions involving angles.

Pythagorean Identity

The Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1. This fundamental relationship allows us to express one trigonometric function in terms of another, facilitating the simplification of expressions. In the given expression, this identity can be used to relate sin²(π/6) and cos²(π/6).

Angle Values

Specific angle values, such as π/6, correspond to known sine and cosine values. For instance, cos(π/6) = √3/2 and sin(π/6) = 1/2. Recognizing these standard values is crucial for evaluating trigonometric expressions quickly and accurately, as they provide the necessary numerical values to compute the expression.