What is the value of tan(2 theta) in terms of tan(theta)?
Answer and explanation
Correct answer: B. 2 tan theta / (1 - tan^2 theta)
- Step 1: Using tan(A + B) = (tan A + tan B) / (1 - tan A tan B) with A = B = theta. Step 2. tan(2 theta) = (2 tan theta) / (1 - tan^2 theta). Answer: 2 tan theta / (1 - tan^2 theta). Why not the others: 2 tan theta / (1 + tan^2 theta) is sin(2 theta); tan^2 theta / (1 - tan theta) is algebraic error; reciprocal is cot(2 theta).
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