First slide

Properties of triangles

Question

In a triangle $\tan A + \tan B + \tan C = 6$ and $\tan A \tan B = 2$ .
Then the values of $\tan A, \tan B a n d \tan C a r e$

Easy

A

1, 2, 3
B

2, 2, 2
C

1, 2, 0
D

None of these

Solution

$S i n c e A + B + C = π in triangle ABC, we have$
$\begin{array}{l} \Rightarrow \tan A + \tan B + \tan C = \tan A \tan B \tan C \\ ⇒ 6 = 2 \tan C \\ ⇒ \tan C = 3 \\ ∴ \tan A + \tan B = 3, \tan A \tan B = 2 \\ ⇒ \tan A = 1 (o r) 2 \\ a n d \tan B = 2 (o r) 1 \end{array}$

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