What is the value of tan 18° ?

• A √5 − 1/√(10 + 2√5)
• B √5 − 1/√(10 + √5)
• C √(10 + 2√5)/√5 − 1
• D √(10 + √5)/√5 − 1

The value of tan 18° can be calculated using trigonometric identities or known values. Among the options provided, the correct expression for tan 18° is:

Correct Answer

A √5 − 1 / √(10 + 2√5)

Explanation

This result can be derived from the half-angle formulas or specific trigonometric values. The angle 18° is related to the pentagon and can be expressed in terms of square roots, leading to the given options.

Why It Matters

Understanding the value of tan 18° is useful in various mathematical contexts, including geometry and calculus, where angles play a crucial role in calculations.