Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises - Page 63: 84

See the answer below.

$\theta$ and $\theta+n\cdot 360^{\circ}$ are coterminal angles. Coterminal angles are angles sharing same initial and terminal sides. Therefore, the values of trigonometric functions of all coterminal angles are same. This implies that $\cos\theta=\cos(\theta+n\cdot360^{\circ}$)