Evaluate: tan(pi/4 + pi/6).
Answer and explanation
Correct answer: B. (1 + sqrt(3)/3) / (1 - sqrt(3)/3) = 2 + sqrt(3)
- Step 1: Use the tangent sum formula: tan(A + B) = (tan A + tan B) / (1 - tan A * tan B).
- Step 2: tan(pi/4) = 1 and tan(pi/6) = 1/sqrt(3). Substituting gives (1 + 1/sqrt(3)) / (1 - 1/sqrt(3)) = (sqrt(3) + 1) / (sqrt(3) - 1) = 2 + sqrt(3).
Answer
(1 + sqrt(3)/3) / (1 - sqrt(3)/3) = 2 + sqrt(3).
Why not the others: 'sqrt(3)' is tan(pi/3); '1 + sqrt(3)' sums the values tan(pi/4) and tan(pi/3) directly without the denominator; '1 / sqrt(3)' is tan(pi/6).
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