Find the Exact Value 2sin(30 degrees )cos(30 degrees )

$2 \sin (30 °) \cos (30 °)$

Apply the sine double-angle identity.

$\sin (2 \cdot 30 °)$

Multiply $2$ by $30 °$ .

$\sin (60)$

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$