Question

If A=${30}^{\circ }$,then: $sin2A=2sinAcosA=\frac{2tanA}{1+ta{n}^{2}A}$
State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

$\sin 2A=2\sin A\cos A=\frac{2\tan A}{1+{\tan }^{2}A}$
Given, $A={30}^{\circ }$
L.H.S : $\sin 2A=\sin 2\times {30}^0=\sin {60}^0=\frac{\sqrt{3}}{2}$
Middle side: $2\sin A\cos A=2\sin {30}^0\cos {30}^0=2\left(\frac{1}{2}\right)\left(\frac{\sqrt{3}}{2}\right)$ = $\frac{\sqrt{3}}{2}$
R.H.S: $\frac{2\tan A}{1+{\tan }^{2}A}=\frac{2\tan {30}^0}{1+{\tan }^2{30}^0}$

= $\frac{2\sqrt{3}}{1+(\sqrt{3}{)}^2}$

= $\frac{2\sqrt{3}}{4}$

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

Hence Proved.