Find the value of `k` if `f(x)` is continuous at `x=pi//2` , where `f(x)={(kcosx)/(pi-2x),\ \ \ x!=pi//2 3,\ \ \ x=pi//2`

Explanation

To find the value of \( k \) such that the function \( f(x) \) is continuous at \( x = \frac{\pi}{2} \), we need to ensure that the limit of \( f(x) \) as \( x \) approaches \( \frac{\pi}{2} \) is equal to the value of the function at \( x = \frac{\pi}{2} \).

### Step-by-Step Solution:

1. **Define the function**:
\[
f(x) =
\begin{cases}
...