Question

\[\frac{2 \tan 30°}{1 - \tan^2 30°}\]  is equal to ______.

Options

• cos 60°

• sin 60°

• tan 60°

• sin 30° 

Answer 1

\[\frac{2 \tan 30°}{1 - \tan^2 30°}\]  is equal to tan 60°.

Explanation:

`(2 tan 30°)/(1-tan^2 30°)`

As, tan 30° = `1/sqrt3`

By substituting the value we get,

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

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

`= 3/sqrt3`

`= (3sqrt3)/3`

`= sqrt3`

And, `sqrt3` = tan 60°.