Answer
True
Work Step by Step
$\sin$(2 * 30$^{\circ}$) = 2 $\sin$ 30$^{\circ}$ * $\cos$ 30$^{\circ}$
First evaluate the value of each trigonometric statement:
$\sin$ (2 * 30$^{\circ}$) = $\sin$ 60$^{\circ}$ = $\frac{\sqrt3}{2}$
$\sin$ 30$^{\circ}$ = $\frac{1}{2}$
$\cos$ 30$^{\circ}$ = $\frac{\sqrt3}{2}$
Next evaluate each side of the equation:
$\sin$( 2 * 30$^{\circ}$) = $\frac{\sqrt3}{2}$
2 $\sin$ 30$^{\circ}$ * $\cos$ 30$^{\circ}$ = 2($\frac{1}{2}$)($\frac{\sqrt3}{2}$)
= $\frac{\sqrt3}{2}$
Therefore:
$\sin$(2 * 30$^{\circ}$) = 2 $\sin$ 30$^{\circ}$ * $\cos$ 30$^{\circ}$ is a true statement.
