Question

The value of (2tan30º)/(1+tan²30º) is *

Answer 1

$\mathfrak{\large{\underline{\underline{Answer}}}} = \bold{ \frac{ \sqrt{3} }{2} }$

Step-by-step explanation:

$\large{ \frac{2 \tan( {30}^{0} ) }{1 + \tan {}^{2} 30 {}^{0} } } \\ \\ = \frac{2 \times \frac{1}{ \sqrt{3} } }{1 + ( { \frac{1}{ \sqrt{3} }) }^{2} } \\ \\ = \frac{ \frac{2}{ \sqrt{3} } }{1 + \frac{1}{3} } \\ \\ \frac{ \frac{2}{ \sqrt{3} } }{ \frac{4}{3} } = \frac{2}{ \sqrt{3} } \times \frac{3}{4} \\ \\ \frac{ \sqrt{3} }{2} = \bold{answer}$

Answer 2

QUESTION:

The value of (2tan30º)/(1+tan²30º) is *

ANSWER:

We know that;

1.

$\huge\orange { \tan(30) = \frac{1}{ \sqrt{3} }}$

2.

$\huge\blue {1 + { \tan( \alpha ) }^{2} = { \sec( \alpha ) }^{2} }$

3.

$\huge\green {\sec(30) = \frac{2}{ \sqrt{3} } }$

now come to main question;

$\frac{2 \times \tan(30) }{1 + { \tan}^{2} 30} \\ \frac{2 \times \frac{1}{ \sqrt{3} } }{ { \sec(30) }^{2} } \\ \frac{ \frac{2}{ \sqrt{3} } }{ { \frac{2}{ \sqrt{3} } }^{2} } \\ \frac{ \frac{2}{ \sqrt{3} } }{ \frac{4}{3} } \\ \frac{2 \times 3}{4 \times \sqrt{3} } \\ \frac{6}{4 \sqrt{3} }$

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

$\red {(rationalisng)}$

$\frac{3 \times 2 \sqrt{3} }{2 \sqrt{3} \times 2 \sqrt{3} } \\ \frac{6 \sqrt{3} }{12} \\ \frac{ \sqrt{3} }{2}$

FINAL ANSWER :

$\huge\pink {\frac{ \sqrt{3} }{2} }$