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Question
If A and B are acute angles such that `tan A = 1/2, tan B = 1/3` and `tan (A + B) = (tan A + tan B)/(1 - tan A tan B)`, find A + B.
Sum
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Solution
`tan A = 1/2, tan B = 1/3`
`tan (A + B) = (tan A + tan B)/(1 - tan A tan B)`
`tan (A + B) = (1/2 + 1/3)/(1 - 1/(2.1/3)) = (5/6)/(1 - 1/6) = 1`
tan (A + B) = tan 45°
∴ A + B = 45°
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