Tangent Double Angle

This identity tells you how to compute the tangent of a double angle using only the tangent of the original angle. It comes from the tangent addition formula by setting the two angles equal: tan(θ+θ), then simplifying the numerator and denominator. The formula is especially useful because it can turn a difficult angle like 2θ into an expression in tan θ alone, though it breaks down when 1 − tan²θ = 0 since the tangent is then undefined.

Use this when you know tan θ and need tan(2θ) without finding the angle itself, especially in trigonometric simplification and proof-based problems. It also appears in calculus, physics, and engineering whenever phase doubling or angle-doubling relationships matter.

• Forgetting to square tan θ in the denominator
• Using tan(2θ) = 2tan θ / (1 + tan²θ), which is the wrong sign
• Ignoring cases where 1 − tan²θ = 0, making the expression undefined