Tangent of a Difference

This identity tells you how to find the tangent of an angle difference using only the tangents of the two angles. It comes from combining the sine and cosine subtraction formulas, then dividing by the cosine of the difference so the result is written as a ratio of tangents. The denominator 1 + tan A tan B appears because the tangent is a quotient, so the cosine terms must be handled carefully.

Use this when you already know tan A and tan B but need tan(A - B) without converting back to the angles themselves. It is especially useful in trigonometric proofs, exact-value calculations, and problems involving angle manipulations in geometry or calculus.

• Using tan(A-B) = tan A - tan B, which ignores the denominator
• Forgetting the plus sign in the denominator 1 + tan A tan B
• Swapping A and B without changing the sign in the numerator