Question

If $A={30}^0$, then $\frac{1-\cos 2A}{\sin 2A}=\tan A$

If above statement is true enter $1$ else $0.$

Answer 1

Given $A={30}^{\circ }$
To Prove: $\frac{1-\cos 2A}{\sin 2A}=\tan A$

L.H.S: $\frac{1-\cos 2A}{\sin 2A}$

= $\frac{1-\cos {60}^0}{\sin {60}^0}$

= $\frac{1-\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

= $\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

= $\frac{1}{\sqrt{3}}$
R.H.S: $\tan A=\tan {30}^0=\frac{1}{\sqrt{3}}$

Thus, $L.H.S=R.H.S$

$\frac{1-\cos 2A}{\sin 2A}=\tan A$ is true when $A={30}^{\circ }$.