Answer
$\lim\limits_{x\to\frac{\pi}{2}}\dfrac{\cos{x}}{\cot{x}}=1.$
Work Step by Step
$\lim\limits_{x\to\frac{\pi}{2}}\dfrac{\cos{x}}{\cot{x}}=\lim\limits_{x\to\frac{\pi}{2}}(\cos{x}\tan{x})=\lim\limits_{x\to\frac{\pi}{2}}\sin{x}=\sin{\frac{\pi}{2}}=1.$
