If in triangle ABC, tan A + tan B + tan C = 6 and tan A tan B = 2, then the triangle is

Right angled isosceles

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Aacute angled isosceles

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Aacute angled

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equilateral

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Solution

The correct option is C Aacute angled
In a $Δ$ ABC, tan A + tan B + tan C = tan A tan B tan C $\Rightarrow$ 6 = 2 tan C $\Rightarrow$ tan C = 3 $\Rightarrow$ tan A + tan B = 3
$\Rightarrow$ tan A = 1, tan B = 2 and tan C = 3 [ $∵$ tan A tan B = 2]

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