Discussion

If \(\tan(A+B) = \sqrt{3}\) and \(\tan(A-B) = \frac{1}{\sqrt{3}}\), find A and B.

Answer: A

From the given information:

1) \(\tan(A+B) = \sqrt{3} \Rightarrow A+B = 60°\)

2) \(\tan(A-B) = \frac{1}{\sqrt{3}} \Rightarrow A-B = 30°\)

We have a system of two linear equations. Adding them gives:

2A = 90° => A = 45°.

Substituting A=45° into the first equation: 45° + B = 60° => B = 15°.

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