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Given tan A = 1/2 and tan B = 1/3, evaluate tan(2A + B) and tan(2A - B).

1. tan(2A + B) = 3 and tan(2A - B) = 1/3
2. tan(2A + B) = 1 and tan(2A - B) = 7
3. tan(2A + B) = 3 and tan(2A - B) = 1
4. tan(2A + B) = 7 and tan(2A - B) = 1/7

Correct answer: tan(2A + B) = 3 and tan(2A - B) = 1/3

Solution

With tan 2A = 4/3 and tan B = 1/3, the sum and difference formulas give tan(2A+B) = 3 and tan(2A-B) = 1/3.

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