Question

2tan30°/1-tan^2 30°=??

Answer 1

we know that tan 2x = 2tan x/1 - tan^2x
there
the given condition can be written as
tan 2(30)
= tan60
= sqrt3

hope it helps

Answer 2

We know, tan 30 = 1/√3
Now, 2×tan30°/1 - tan²30°
$\frac{2 \times \frac{1}{ \sqrt{3} } }{1 - { \frac{1}{ \sqrt{3} } }^{2} }$
$\frac{ \frac{2}{ \sqrt{3} } }{1 - \frac{1}{3} }$
$\frac{ \frac{2}{ \sqrt{3} } }{ \frac{2}{3} }$
$\frac{2 \times 3}{2 \times \sqrt{3} }$
$\sqrt{3}$