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If A = tan⁻¹ ((x√(3))/(2K-x)) and B = tan⁻¹ ((2x-K)/(K√(3))), then what is the value of A - B?

1. 0°
2. 45°
3. 60°
4. 30°

Correct answer: 30°

Solution

Writing tan A = x*sqrt3/(2K-x) and tan B = (2x-K)/(K*sqrt3), then tan(A-B) = (tanA - tanB)/(1+tanA tanB) reduces to 1/sqrt3, so A - B = 30 degrees.

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