Question

tan 2A = 3 tan A is true, when the measure of ∠A is ______.

Options

• 90°

• 60°

• 45°

• 30°

Answer 1

tan 2A = 3 tan A is true when the measure of ∠A is 30°.

Explanation:

tan 2A = 3 tan A

`(2 tan A)/(1 - tan^2 A)` = 3 tan A

2 tan A = 3 tan A (1− tan² A)

`2/3` = 1 − tan² A

tan² A = `1 − 2/3`

tan² A = `1/3`

tan A = `1/sqrt3`

tan A = tan 30

A = 30°