If $\;f(\theta) = \begin{vmatrix} 1 & cos\theta &1 \\[0.3em] -sin\theta & 1 & \cos \theta \\[0.3em] -1 & sin \theta & 1\end{vmatrix}\;$ and A and B are respectively the maximum and the minimum values of $\;f(\theta)\;$ , then (A ,B) is equal to :

Question

$(a)\;(3 ,-1)\qquad(b)\;(4,2 -\sqrt{2})\qquad(c)\;(2 +\sqrt{2} ,2 -\sqrt{2})\qquad(d)\;(2 +\sqrt{2},-1)$