Question

Choose the correct option and justify your choice:
$\sin 2A=2\sin A$ is true when $A=$

• A. $0^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A $0^{\circ }$

$\sin 2A=2\sin A$ ....given

$2\sin A\cos A=2\sin A$ ($\because \sin 2A=2\sin A\cos A$)

$2\sin A\cos A-2\sin A=0$

$2\sin A(\cos A-1)=0$

Either $\sin A=0$ or $\cos A-1=0$

$A=0^{\circ }$ or $\cos A=1⟹A=0^{\circ }$

Hence, option A is correct.