Question

The value of $\cos (2\times {30}^0)=\frac{1-{\tan }^2{30}^0}{1+{\tan }^2{30}^0}$

If true then enter $1$ 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.: $\frac{1-{\tan }^2{30}^0}{1+{\tan }^2{30}^0}$
= $\frac{1-(\frac{1}{\sqrt{3}}{)}^2}{1+\left(\frac{1}{\sqrt{3}}{)}^2\right)}$
= $\frac{\frac{2}{3}}{\frac{4}{3}}$
= $\frac{1}{2}$
Thus, $L.H,S.=R.H.S$