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In triangle ABC, the ratio tanA: tanB: tanC = 1: 2: 1. Find the value of tanA*tanC + tanB*tanC + tanA*tanB.

1. 10
2. 8
3. 6
4. 12

Correct answer: 10

Solution

With tanA=t, tanB=2t, tanC=t, the identity gives 4t = 2t³, so t²=2. Then tanA*tanC + tanB*tanC + tanA*tanB = t² + 2t² + 2t² = 5t² = 10.

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