Question

`(2 tan 30°)/(1-tan^2 30°)` = ______.

Options

• cos 60°

• sin 60°

• tan 60°

• sin 30°

Answer 1

`(2 tan 30°)/(1-tan^2 30°)` = tan 60°

Explanation:

`(2 tan 30°)/(1-tan^2 30°)`

= `(2(1/sqrt3))/(1-(1/sqrt3)^2)`

= `(2/sqrt3)/(1-1/3)`

= `(2/sqrt3)/(2/3)`

= `sqrt3`

Out of the given alternatives, only tan 60° = `sqrt3`

Hence, tan 60° is correct.