In a triangle tan A + tan B + tan C = 6 and tan Atan B = 2, then values of tan A,,,tan B and tan C a

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3.Trigonometrical Ratios, Functions and Identities

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In a triangle $\tan A + \tan B + \tan C = 6$ and $\tan A\tan B = 2,$ then the values of $\tan A,\,\,\tan B$ and $\tan C$ are

A

$1, 2, 3$

B

$2,1,3$

C

$(a)$ and $(b)$ both

D

None of these

Solution

(c) $\tan A + \tan B + \tan C = \tan A\tan B\tan C$

$\therefore \tan A\tan B\tan C = 6 \Rightarrow \tan C = \frac{6}{2} = 3$

Also $\tan A + \tan B = 6 – 3 = 3$

$\therefore \tan A,\tan B = 2,1$ or $1, 2$ and $\tan C = 3$.

Standard 11

Mathematics

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