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Given tan(alpha) = 5/6 and tan(beta) = 1/11, prove that alpha + beta = pi/4.

1. True: tan(alpha+beta) = 1, so alpha+beta = pi/4 (proved)
2. False
3. alpha + beta = pi/3
4. alpha + beta = pi/6

Correct answer: True: tan(alpha+beta) = 1, so alpha+beta = pi/4 (proved)

Solution

tan(alpha+beta) = (5/6 + 1/11)/(1 - 5/66) = (61/66)/(61/66) = 1, so alpha+beta = pi/4.

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