Question

Please Answer this question​

Answer 1

Step-by-step explanation:

refer the attachment above

Answer 2

To find:

$\dfrac{2\tan30^\circ}{1-\tan^2 30^\circ}$

Solution:

By putting value of tan30°=1\√3

$\Longrightarrow\dfrac{2\times\dfrac{ 1} {\sqrt3}}{1-\bigg(\dfrac{1}{\sqrt3}\bigg)^2}$

$\Longrightarrow\dfrac{\dfrac{ 2} {\sqrt3}}{1-\dfrac{1}{3}}$

Now taking LCM in denominator

$\Longrightarrow\dfrac{\dfrac{ 2} {\sqrt3}}{\dfrac{3-1}{3}}$

$\Longrightarrow\dfrac{\dfrac{ 2} {\sqrt3}}{\dfrac{2}{3}}$

$\Longrightarrow{\dfrac{ 2\times3} {2\times\sqrt3}}$

Now 2 will be cancelled from numerator and denominator

$\Longrightarrow{\dfrac{ 3} {\sqrt3}}$

Now divide √3 from numerator and denominator

$\Longrightarrow{\dfrac{ 3\div\sqrt3} {\sqrt3\div\sqrt3}}$

$\Longrightarrow{\dfrac{\sqrt3}{1}}$

$\Longrightarrow \sqrt3$

So the required Answer is √3.