Chapter 4 - Section 4.5 - Indeterminate Forms and L'Hôpital's Rule - Exercises - Page 248: 70

$1$

Here, $\lim\limits_{x \to 0^{+}} f(x)=\lim\limits_{x \to \dfrac{\pi}{2}^{-}} \dfrac{\cot x}{\csc x}$ This implies that $\lim\limits_{x \to 0^{+}} (\dfrac{cos x/\sin x}{1/\sin x})=\lim\limits_{x \to 0^{+}} \dfrac{\cos x}{\sin x}(\sin x)$ Thus, $\cos (0)=1$