If [x] denotes the greatest integer not exceeding x and if the function f defined by $$f(x) = \left\{ \begin{array}{l l} \frac{a+2 \cos x}{x^2} & \quad ( x < 0) \\ b\;\tan \frac{\pi}{[x+4]} & \quad (x \geq 0) \end{array} \right.$$ is continuous at $x=0,$ then the ordered pair $(a,b)=$

Question

$$(a)\;(-2,1) \quad (b)\;(-2,-1) \quad (c)\;(-1,\sqrt 3) \quad (d)\;(-2, -\sqrt 3)$$