## The Proof of the Tangent Half-Angle Formula

In this post, we prove the following trigonometric identity:

.

**Proof**

Consider a semi-circle with “center” and diameter and radius equal to 1 unit as shown below. If we let , then by the Inscribed Angle Theorem, .

Draw perpendicular to as shown in the second figure. We can compute for the sine and cosine of which equal to the lengths of and , respectively. In effect, and . » Read more