If tan α = $\frac{1}{2}$ and tan β = $\frac{1}{3}$ and both α and β are acute, find tan (α + β).

Analyze the question: You are given tan α and tan β and asked for tan (α + β). This calls for the tangent addition formula.

Concept:

tan(α + β) = (tan α + tan β) / (1 − tan α · tan β)

Solution:

1. Numerator: 1/2 + 1/3 = 3/6 + 2/6 = 5/6
2. Denominator: 1 − (1/2)(1/3) = 1 − 1/6 = 5/6
3. Divide: tan(α + β) = (5/6) ÷ (5/6) = 1

Since tan(α + β) = 1, α + β = 45°, which makes sense because both angles are acute and fairly small (about 26.6° and 18.4°, which add up to 45°).

Answer: B (1)

Tip: Note that option E (45) is the angle, not the tangent value. Examiners include this kind of trap, so always check whether the question asks for the ratio or the angle. Also remember the sign pattern: the numerator has a plus, and the denominator has a minus, for tan(α + β).