Find the Exact Value 2sin(105 degrees )cos(105 degrees )

$2 \sin (105 °) \cos (105 °)$

Apply the sine double-angle identity.

$\sin (2 \cdot 105 °)$

Multiply $2$ by $105 °$ .

$\sin (210)$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.

$- \sin (30)$

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

$- \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$

Find the Exact Value 2sin(105 degrees )cos(105 degrees )

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