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If A + B + C = pi/2, find the value of tan(A)*tan(B) + tan(B)*tan(C) + tan(C)*tan(A).

1. 1
2. 0
3. -1
4. 1/2

Correct answer: 1

Solution

From A+B = pi/2 - C, tan(A+B) = cot(C); cross-multiplying gives tanA tanC + tanB tanC = 1 - tanA tanB, which rearranges to the required sum equal to 1.

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