Find the Exact Value 2sin(75 degrees )cos(75 degrees )

$2 \sin (75 °) \cos (75 °)$

Step 1

Apply the sine double-angle identity.

$\sin (2 \cdot 75 °)$

Step 2

Multiply $2$ by $75 °$ .

$\sin (150)$

Step 3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (30)$

Step 4

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$