Which identity correctly represents the relation of tan(α - β)?

The correct representation of the relation for tan(α - β) is formulated based on the angle subtraction formula for tangent. The relevant identity states that when subtracting two angles, the tangent of the difference is derived from the tangents of the individual angles.

The proper identity is given as:

tan(α - β) = (tan α - tan β) / (1 + tan α tan β).

This is correct because it captures the essence of how tangent behaves under subtraction. When subtracting angles in trigonometry, the relationship between the tangents of the angles depends critically on their individual tangent values while also involving the product of these tangent values in the denominator to maintain the identity's validity.

The plus sign in the denominator is crucial because it reflects the behavior of the tangent function, where the addition of two angles is inherently related to their respective tangents. This formulation holds up under various conditions and satisfies the expected results for specific angle measurements.

Understanding this identity is important for solving equations or simplifying expressions involving tangent, particularly in various applications such as solving trigonometric equations or analyzing angular relationships in geometry.