)The Tangent Half-Angle Identity is a trigonometric identity that relates the tangent of a half-angle to the tangent of the original angle.
The formula for the Tangent Half-Angle Identity is tan(θ/2) = ±√[(1-cosθ)/(1+cosθ)].
The Tangent Half-Angle Identity is used to simplify trigonometric expressions and solve trigonometric equations involving half-angles.
The Tangent Half-Angle Identity can be derived using the double angle formula for tangent and the Pythagorean identity for sine and cosine.
The ± symbol indicates that there are two possible solutions for the tangent of the half-angle, depending on the quadrant of the original angle. This allows for the use of the Tangent Half-Angle Identity in all four quadrants.