If `(lim)_(x->0)k x\ cosec\ x=(lim)_(x->0) xcosec\ k x `, find `k`

Explanation

To solve the problem, we need to evaluate the limit expression given and find the value of \( k \) such that:

\[ \lim_{x \to 0} kx \cdot \csc x = \lim_{x \to 0} x \cdot \csc(kx) \]

### Step 1: Rewrite the Cosecant Function
We know that \( \csc x = \frac{1}{\sin x} \). Therefore, we can rewrite the limits as follows:
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