Question

CHOOSE THE CORRECT ANSWER FROM THE FOLLOWING ALTERNATIVES

2tan30°/1+tan2 30°​

Answer 1

Step-by-step explanation:

$\frac{2tan \: 30}{1 + {tan}^{2} \: 30}$

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

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

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

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

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

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