The value of [tex]\lim_{x \to a} \sqrt{a^2-x^2} \cot \left(\frac{\pi}{2} \cdot \sqrt{\frac{a-x}{a+x}} \right)[/tex] is
A) [tex]\frac{2a}{\pi}[/tex]
B) [tex]-\frac{2a}{\pi}[/tex]
C) [tex]\frac{4a}{\pi}[/tex]
D) [tex]-\frac{4a}{\pi}[/tex]​