Question

$\sin 2A=2\sin A$ is true when $A=$

• A. $30°$
• B. $0°$
• C. $45°$
• D. $90°$

Answer 1

The correct option is B

$0°$

Consider $\sin 2A=2\sin A.....\left(i\right)$

We know that $\sin 2A=2\sin A\cos A....\left(ii\right)$

Substitute $\left(ii\right)$ in $\left(i\right)$, we get

$$\begin{gathered} \sin 2A=2\sin A \\ \Rightarrow 2\sin A\cos A=2\sin A \\ \Rightarrow \cos A=1 \\ but\cos 0°=1 \\ \Rightarrow A=0° \end{gathered}$$

Hence, $\sin 2A=2\sin A$ is true when $A=0°$