Thomas' Calculus 13th Edition

The results agree with the fact that the cosine and sine functions are periodic with a period of $2\pi$
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 $2\pi$