Let f(x) = \(\begin{cases}
\cfrac{k\,cos\,\text x}{\pi-2\text x}, \quad \text x\neq \cfrac{\pi}2 \\
3,\quad\text x=\cfrac{\pi}2
\end{cases}
\)
{(k cos x)/(π - 2x), x ≠ π/2, 3, x = π/2.
If \(\lim\limits_{\text x \to\pi/2}
\) f(x) = f\(\left(\cfrac{\pi}2\right)\),
lim(x→π/2) f(x) = f(π/2),
find the value of k.
