Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 692: 5

$5\rightarrow F$

$2\sin \alpha \cos \alpha =\sin _{2}\alpha \Rightarrow 4\sin \dfrac {\pi }{3}\cos \dfrac {\pi }{3}=2\times \left( 2\sin \dfrac {\pi }{3}\cos \dfrac {\pi }{3}\right) =2\times \sin \dfrac {2\pi }{3}=2\times \dfrac {\sqrt {3}}{2}=\sqrt {3}\Rightarrow $ $5\rightarrow F$