Question

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

Options

• sin 60°

• cos 60°

• tan 60°

• sin 30°

• sec 60°

• cosec 60°

Answer 1

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

Explanation:

We have to find the value of the following expression

`(2 tan 3θ°)/(1+ tan^2 30°)`

`(2 tan 30°)/(1+tan ^2 30°)`

=`(2xx1/sqrt3)/(1+(1/sqrt3))`

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

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

Since tan 60°=`sqrt3/2`, since tan 30°= `1/sqrt3`

=`sqrt3/2`

= `sin 60°`