Question

Find the Value of
$\frac{2 \tan(30) }{1+ { \tan(30) }^{2} }$
​

Answer 1

find your answer in image

answer can be written in 3 ways

first root 3 by 2

second sin60°

third cos30°

Answer 2

$\frac{2 \tan(30) }{1+ { \tan(30) }^{2} }$

We Know that

Tan 30°= $\frac{1}{ \sqrt{3} }$

So,

$\frac{2 \tan(30) }{1+ { \tan(30) }^{2} }$

$= > \frac{2 \frac{1}{ \sqrt{3} } }{1 + {( \frac{1}{ \sqrt{3} } )}^{2} }$

$= > \frac{ \frac{2}{ \sqrt{3} } }{1 + \frac{1}{3} }$

$= > \frac{ \frac{2}{ \sqrt{3} } }{ \frac{3 + 1}{3} }$

$= > \frac{ \frac{2}{ \sqrt{3} } }{ \frac{4}{3} }$

$= > \frac{3}{ \sqrt{3 } \times 2}$

$= > \frac{ \sqrt{3} \times \sqrt{3} }{ \sqrt{3} \times 2}$

$= > \frac{ \sqrt{3} }{2}$