Question

216 $\lim_{x \to \pi / 2} \frac{\cot x}{\cos x}$

Explanation:

Step1: Rewrite cotangent

Recall that \(\cot x=\frac{\cos x}{\sin x}\). So \(\frac{\cot x}{\cos x}=\frac{\frac{\cos x}{\sin x}}{\cos x}\).
Simplify the expression: \(\frac{\frac{\cos x}{\sin x}}{\cos x}=\frac{1}{\sin x}\) (for \(x
eq n\pi\), \(n\in\mathbb{Z}\)).

Step2: Evaluate the limit

Now we need to find \(\lim_{x
ightarrow\frac{\pi}{2}}\frac{1}{\sin x}\).
Substitute \(x = \frac{\pi}{2}\) into \(\frac{1}{\sin x}\). Since \(\sin\frac{\pi}{2}=1\).

Answer:

\(1\)