Question

If $\angle x={30}^0$, then $\tan 2x=\frac{2\tan x}{1-{\tan }^{2}x}$.

If true enter 1 else 0.

Answer 1

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

$=\frac{2\tan {30}^o}{1-{\tan }^2{30}^o}$

$=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1-(\frac{1}{\sqrt{3}}{)}^2}$

$=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{\frac{2}{3}}$

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