Use a calculator to decide whether the statement is true or false. \[ \sin 64^{\circ}=2 \cos 16^{\circ} \sin 16^{\circ} \] The statement \( \sin 64^{\circ}=2 \cos 16^{\circ} \sin 16^{\circ} \) is \( \square \mathbf{\nabla} \)

To evaluate the statement, we'll first calculate both sides using a calculator. The left side is simply \(\sin 64^\circ\). On the right side, we first need to calculate \(\cos 16^\circ\) and \(\sin 16^\circ\), and then use those values to find \(2 \cos 16^\circ \sin 16^\circ\). Calculating \(\sin 64^\circ \approx 0.8988\). Next, calculate: \(\cos 16^\circ \approx 0.9613\) and \(\sin 16^\circ \approx 0.2764\). Now, calculate the right side: \[ 2 \cos 16^\circ \sin 16^\circ \approx 2 \cdot 0.9613 \cdot 0.2764 \approx 0.5314 \]. Now compare both sides: \[ \sin 64^\circ \approx 0.8988 \quad \text{and} \quad 2 \cos 16^\circ \sin 16^\circ \approx 0.5314 \]. Since \(0.8988 \neq 0.5314\), the statement \( \sin 64^\circ=2 \cos 16^\circ \sin 16^\circ \) is **false**.