If in triangle ABC - tan A -tan B -tan C -6 and tan A tan B -2- then the triangle isA- Acute angledB- equilateralC- Right angled isoscelesD- Acute angled isosceles

The correct option is A Acute angledIn a ΔABC, tan A + tan B + tan C = tan A tan B tan C ⇒ 6 = 2 tan C ⇒ tan C = 3 ⇒ tan A + tan B = 3 ⇒ tan A = 1, tan B = 2 ...

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Standard XI

Mathematics

Fundamental Laws of Logarithms

If in triangl...

Question

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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Acute angled isosceles

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Acute angled

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equilateral

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Solution

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

The correct option is C Acute angledIn a ΔABC, tan A + tan B + tan C = tan A tan B tan C ⇒ 6 = 2 tan C ⇒ tan C = 3 ⇒ tan A + tan B = 3 ⇒ tan A = 1, tan B = 2 and tan C = 3 [∵ tan A tan B = 2]

The correct option is C Acute 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]