Find the Exact Value sin(2arccos(( square root of 2)/2))

$\sin (2 \arccos (\frac{\sqrt{2}}{2}))$

The exact value of $\arccos (\frac{\sqrt{2}}{2})$ is $\frac{π}{4}$ .

$\sin (2 \frac{π}{4})$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\sin (2 \frac{π}{2 (2)})$

Cancel the common factor.

$\sin (2 \frac{π}{2 \cdot 2})$

Rewrite the expression.

$\sin (\frac{π}{2})$

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

$1$