What is the value of the expression: arctan(1/2) + arctan(1/3)?
Answer and explanation
Correct answer: C. pi / 4 (45 degrees)
- Step 1: Identity: arctan(x) + arctan(y) = arctan((x + y) / (1 - xy)) for xy < 1. Step 2. Numerator = 1/2 + 1/3 = 5/6. Step 3. Denominator = 1 - (1/2 1/3) = 1 - 1/6 = 5/6. Step 4. Ratio = (5/6) / (5/6) = 1. arctan(1) = pi / 4. Answer: pi / 4 (45 degrees). Why not the others: Classic trigonometric identity yielding 45 degrees.
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