Question

$tan(2\times {30}^{\circ })=\frac{2tan{30}^{\circ }}{1-ta{n}^2{30}^{\circ }}$, if true then write 1 and if false then write 0

Answer 1

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