Question

In any ΔABC, if 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 ______.

Options

• 1, 2, 3

• 0, 1, 2

• 1, 2, 0

• None of these

Answer 1

In any ΔABC, if 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 1, 2, 3.

Explanation:

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

∴ tan A tan B tan C = 6

`\implies` tan C = `6/2` = 3

Also, tan A + tan B = 6 – 3 = 3

∴ tan A, tan B = 2, 1 or 1, 2 and tan C = 3