Question

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

Answer 1

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