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In triangle ABC, if angle A = tan⁻¹(2) and angle B = tan⁻¹(3), then angle C equals

1. π/3
2. π/4
3. π/6
4. 3π/4

Correct answer: π/4

Solution

tan^-1 2 + tan^-1 3 = 3pi/4 (since the tangent sum (2+3)/(1-6) = -1 and both angles lie in the first quadrant). Then C = pi - A - B = pi - 3pi/4 = pi/4.

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