Answer
See the steps.
Work Step by Step
$\sin{(x+2 \pi )} = \sin{x} \cos{2 \pi} + \cos{x} \sin{2 \pi}$
$\sin{(x+2 \pi )} = \sin{x} \times 1 + \cos{x} \times 0 = \sin{x}$
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