Question

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

Answer 1

$\sin (2\times {30}^0)=\frac{2\tan {30}^0}{1+{\tan }^2{30}^0}$
L.H.S :$\sin (2\times {30}^0)$
= $\sin \left({60}^0\right)$
= $\frac{\sqrt{3}}{2}$
R.H.S: $\frac{2\tan {30}^0}{1+{\tan }^2{30}^0}$
= $\frac{2\frac{1}{\sqrt{3}}}{1+\frac{1}{3}}$
= $\frac{2\frac{1}{\sqrt{3}}}{\frac{3+1}{3}}$
= $\frac{2\frac{1}{\sqrt{3}}}{\frac{4}{3}}$
= $\frac{\sqrt{3}}{2}$
Thus, $L.H.S=R.H.S$