Question

2tan30/1+tan^2 30......?​

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

$\sf{\dfrac{2tan30}{1+tan^{2} 30}}$

Using Identity :-

$\sf{\dfrac{2tanx}{1 + tan^{2} x} = Sin(2x)}$

$\sf{Here \: ,}$

$\sf{x = 30}$

$\sf{So}$

$\sf{Sin 2(30)}$

$\sf{Sin60}$

$\sf{\dfrac{\sqrt{3}}{2}}$

Other Related Identities :-

1)$\sf{\dfrac{2tanx}{(1-tan^{2} x)} = tan2x}$

2)$\sf{\dfrac{(1-tan^{2} x)}{(1+tan^{2} x} = Cos2x}$