Question

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

Options

• sin 60°

• cos 60°

•  tan 60°

• sin 30°

Answer 1

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°`