Answer
The results agree with the fact that the cosine and sine functions are periodic with a period of $2\pi$
Work Step by Step
Addition formulas
$$\cos{(A+B)}= \cos{A} \cos{B}-\sin{A}\sin{B}$$
$$\sin{(A+B)}= \sin{A} \cos{B} +\cos{A} \sin{B}$$
$\cos{(A+2\pi)} = \cos{A} \cos{2\pi} -\sin{A} \sin{2\pi}$
$\cos{(A+2\pi)} = \cos{A} \times (1) - \sin{A} \times (0)$
$\cos{(A+2\pi)} = \cos{A}$
$\sin{(A+2\pi)} = \sin{A} \cos{2\pi} + \cos{A} \sin{2\pi}$
$\sin{(A+2\pi)} = \sin{A} \times (1) + \cos{A} \times (0)$
$\sin{(A+2\pi)} = \sin{A} $
The results agree with the fact that the cosine and sine functions are periodic with a period of $2\pi$
