Question

`(2 tan 30°)/(1+tan^2 30°)` = ______.

Options

• sin 60°

• cos 60°

• tan 60°

• sin 30°

Answer 1

`(2 tan 30°)/(1+tan^2 30°)` = sin 60°.

Explanation:

`(2 tan 30°)/(1+tan^2 30°)`

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

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

= `(2/sqrt3)/(4/3)`

= `6/(4sqrt3)`

= `sqrt3/2`

Out of the given alternatives, only sin 60° = `sqrt3/2`