If in a ABC - tan A -tan B -tan C -6- then A B cot C -A- 6B- 1C- none of theseD- 1-6

The correct option is D 1/6 In triangle ABC, A+B+C= π We know that tan(A+B+C) = tanA+tanB+tanC tanAtanBtanC/1 tanAtanB tanBtanC tanCtanA and tan π = 0 ∴ tanA+ ...

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Standard XII

Mathematics

Conditional Identities

If in a ABC ,...

Question

If in a $△ A B C,$ tanA+tanB+tanC =6, then cotA cotB cotC=

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\frac{1}{6}

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none of these

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Solution

The correct option is C $\frac{1}{6}$

In triangle ABC,
$A + B + C = π$
We know that tan(A+B+C)
$= \frac{t a n A + t a n B + t a n C - t a n A t a n B t a n C}{1 - t a n A t a n B - t a n B t a n C - t a n C t a n A}$
and $t a n π = 0$
$∴ t a n A + t a n B + t a n C - t a n A t a n B t a n C = 0$
tanA + tanB + tanC = tanA tanB tanC
If tanA + tanB + tanC = 6
tanA tanB tanC = 6
$\Rightarrow \frac{1}{t a n A t a n B t a n C} = \frac{1}{6}$
$\Rightarrow c o t A c o t B c o t C = \frac{1}{6}$

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