Question

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

• A. 1,2,3
• B. 2, 1, 3
• C. 1, 2, 0
• D. 1, 2, 2

Answer 1

Answer: (A), (B)

The correct options are
A

1,2,3

B

2, 1, 3

tan A + tan B +tan C = 6 - - - - - - (1)

In a triangle A + B + C = ${180}^{\circ }$

A + B = 180 - C

We see all the terms include tan function

Let's take tan on both sides

tan (A + B) = tan (180 - C)

$\frac{tanA+tanB}{1-tanA.tanB}$ = -tanC

tan A + tan B = - tan C + tan A tan B tan C

tan A + tan B + tan C = tan A tan B tan C - - - - - - (2)

Given tan A .tan B = 2 & tan A + tan B + tan C = 6

From equation 1 & equation 2

tan A $\times$ tan B $\times$ tan C = 6

2 $\times$ tan C = 6

tan C = 3

tan A . tan B = 2, tan A + tan B = 3

tanA = 1 and tanB = 2 or tanA = 2 and tanB = 1.

So, both options A & B are correct