Question

If x = ${30}^{\circ }$, verify that :
$tan2x=\frac{2tanx}{1-ta{n}^{2}x}$
if true then write 1 and if false then write 0

Answer 1

Given: $x={30}^0$,
To Prove: $\tan 2x=\frac{2\tan x}{1-{\tan }^{2}x}$
L.H.S: $\tan 2x=\tan {60}^0=\sqrt{3}$
R.H.S: $\frac{2\tan x}{1-{\tan }^{2}x}$
= $\frac{2\tan {30}^0}{1-{\tan }^2{30}^0}$
= $\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1-(\frac{1}{\sqrt{3}}{)}^2}$
= $\frac{2\left(\frac{1}{\sqrt{3}}\right)}{\frac{2}{3}}$

= $\sqrt{3}$
Thus, $L.H.S.=R.H.S$

Hence 1 is answer